{"segments": [{"id": 1, "seek": 2618, "start": 0.72, "end": 26.18, "text": "بسم الله الرحمن الرحيم اليوم ان شاء الله نكمل في شتة تمانية techniques of integration طرق التكامل سبشن تمانية اتنين اللي نحكي اليوم عن ال trigonometric integrals يعني التكاملات اللي فيها لل trigonometric functions اللي هي الاقترانات المثلثية ال trigonometric integrals راح يكون في عندنا راح ناخد الأنواع تبعتها كلها إذا كانت تكامل sine في cosine", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 16472, 13412, 16606, 21984, 8717, 24793, 1211, 8978, 13412, 2655, 3660, 46811, 7649, 10632, 7512, 295, 10980, 23032, 2288, 4587, 16712, 4117, 10943, 1211, 8608, 3555, 8592, 1863, 46811, 7649, 10632, 1975, 2655, 1863, 9957, 13672, 1829, 8717, 5016, 4117, 1829, 45595, 20498, 18871, 2423, 35386, 266, 29470, 3572, 1124, 37495, 22653, 16712, 4117, 10943, 1211, 9307, 13672, 1829, 8978, 11296, 24976, 35386, 266, 29470, 6828, 13672, 1829, 39896, 42963, 38149, 2288, 7649, 9307, 9673, 12984, 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"probability": 0.852783203125}, {"start": 141.08, "end": 141.24, "word": " N", "probability": 0.77734375}, {"start": 141.24, "end": 141.42, "word": " بدنا", "probability": 0.758544921875}, {"start": 141.42, "end": 141.86, "word": " نحطها", "probability": 0.9814453125}, {"start": 141.86, "end": 142.32, "word": " كزين", "probability": 0.9850260416666666}, {"start": 142.32, "end": 142.48, "word": " أس", "probability": 0.972900390625}, {"start": 142.48, "end": 142.9, "word": " 2K", "probability": 0.76611328125}, {"start": 142.9, "end": 143.04, "word": " زا", "probability": 0.982666015625}, {"start": 143.04, "end": 143.16, "word": " إد", "probability": 0.947998046875}, {"start": 143.16, "end": 143.52, "word": " واحد", "probability": 0.974853515625}, {"start": 143.52, "end": 144.12, "word": " كزين", "probability": 0.9518229166666666}, {"start": 144.12, "end": 144.5, "word": " واحدة", "probability": 0.9798177083333334}, {"start": 144.5, "end": 144.68, "word": " بدنا", "probability": 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"end": 183.76, "text": "طيب إذا كانت لا ال M ولا ال N ولا واحدة منهم odd التنتين even إذا كانت ال M و ال N are both even ففي هذه الحالة بنستخدم .. بنحول ال sine تربيع .. ال sine تربيع بنحولها لقانون ضئف الزاوية و ال cosine تربيع برضه بنحولها لقانون ضئف الزاوية بهذا الشكل و بنضربهم في بعض و بنشوف إيش بيطلع معانا شغلانة بنشوف الأمثلة على هذا النوع", "tokens": [9566, 1829, 3555, 11933, 15730, 25961, 2655, 20193, 2423, 376, 49429, 2423, 426, 49429, 36764, 24401, 3660, 9154, 16095, 7401, 16712, 29399, 9957, 754, 11933, 15730, 25961, 2655, 2423, 376, 4032, 2423, 426, 366, 1293, 754, 6156, 41185, 29538, 21542, 6027, 3660, 44945, 14851, 9778, 40448, 4386, 44945, 5016, 12610, 2423, 18609, 6055, 2288, 21292, 3615, 4386, 2423, 18609, 6055, 2288, 21292, 3615, 44945, 5016, 12610, 11296, 5296, 4587, 7649, 11536, 48812, 19986, 5172, 6024, 110, 995, 2407, 10632, 4032, 2423, 23565, 6055, 2288, 21292, 3615, 4724, 43042, 3224, 44945, 5016, 12610, 11296, 5296, 4587, 7649, 11536, 48812, 19986, 5172, 6024, 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"text": "من التكامل اول اشي evaluate التكامل ل sin تكييب cos تربيع الان بتلاحظ نتطلع بالاول حتى لو كانت هذه التنتين اوضة احنا بناخد هذه اوضة والتانية مالنجدعو فيها even او odd الان مدام ال sign مرفوعة اوضة اوضة بنتعامل معها هي اللي بالاول فمدام ال sign اوضة اوضة يبقاش ناخد sign واحدة ناخد sign واحدة بيظل عندنا هنا sign تربيع ال sign تربيع بنروح بنحولها للقانون اللي هو واحد ناقص cosine تربيع", "tokens": [27842, 16712, 4117, 10943, 1211, 1975, 12610, 1975, 8592, 1829, 13059, 16712, 4117, 10943, 1211, 5296, 3343, 6055, 4117, 1829, 1829, 3555, 3792, 6055, 2288, 21292, 3615, 2423, 7649, 39894, 15040, 5016, 19913, 8717, 2655, 9566, 1211, 3615, 20666, 995, 12610, 11331, 49975, 45164, 25961, 2655, 29538, 16712, 29399, 9957, 1975, 2407, 11242, 3660, 1975, 5016, 8315, 44945, 47283, 3215, 29538, 1975, 2407, 11242, 3660, 16070, 2655, 7649, 10632, 3714, 6027, 1863, 7435, 3215, 3615, 2407, 8978, 11296, 754, 1975, 2407, 7401, 2423, 7649, 3714, 3215, 10943, 2423, 1465, 3714, 28480, 2407, 27884, 1975, 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0.931640625}, {"start": 205.24, "end": 205.8, "word": " ناخد", "probability": 0.86376953125}, {"start": 205.8, "end": 206.02, "word": " sign", "probability": 0.84326171875}, {"start": 206.02, "end": 206.32, "word": " واحدة", "probability": 0.9855143229166666}, {"start": 206.32, "end": 206.56, "word": " بيظل", "probability": 0.63348388671875}, {"start": 206.56, "end": 206.76, "word": " عندنا", "probability": 0.662109375}, {"start": 206.76, "end": 206.94, "word": " هنا", "probability": 0.92041015625}, {"start": 206.94, "end": 207.18, "word": " sign", "probability": 0.39111328125}, {"start": 207.18, "end": 207.7, "word": " تربيع", "probability": 0.9564208984375}, {"start": 207.7, "end": 208.12, "word": " ال", "probability": 0.89404296875}, {"start": 208.12, "end": 208.36, "word": " sign", "probability": 0.87744140625}, {"start": 208.36, "end": 208.82, "word": " تربيع", "probability": 0.9273681640625}, {"start": 208.82, "end": 209.12, "word": " بنروح", "probability": 0.8927408854166666}, {"start": 209.12, "end": 209.82, "word": " بنحولها", "probability": 0.8497314453125}, {"start": 209.82, "end": 210.94, "word": " للقانون", "probability": 0.96484375}, {"start": 210.94, "end": 211.08, "word": " اللي", "probability": 0.776123046875}, {"start": 211.08, "end": 211.22, "word": " هو", "probability": 0.98193359375}, {"start": 211.22, "end": 211.48, "word": " واحد", "probability": 0.9287109375}, {"start": 211.48, "end": 211.8, "word": " ناقص", "probability": 0.966552734375}, {"start": 211.8, "end": 212.2, "word": " cosine", "probability": 0.45947265625}, {"start": 212.2, "end": 212.68, "word": " تربيع", "probability": 0.9298095703125}], "temperature": 1.0}, {"id": 11, "seek": 23617, "start": 213.09, "end": 236.17, "text": "وفي cos تربيع وهذا الـ sine بنخلّيها هيك بين أُسين معين DX عشان هي بنتكون DU الأن هنا ده في cos تربيع بنروح بنفتك الأُس بندخل ال cos تربيع على الأُس بيصير cos تربيع ناقص cos أربعة في sine X DX الأن هنا بيصير ال cosine كأنها هي U هي DU موجودة بس بالسالم يبقى لو أخدنا U تساوي cosine تبقى DU تساوي ناقص sine", "tokens": [38688, 1829, 3792, 6055, 2288, 21292, 3615, 37037, 15730, 2423, 39184, 18609, 4724, 1863, 9778, 1211, 11703, 1829, 11296, 39896, 4117, 49374, 5551, 10859, 3794, 9957, 20449, 9957, 48817, 6225, 8592, 7649, 39896, 4724, 29399, 30544, 28423, 16247, 1863, 34105, 11778, 3224, 8978, 3792, 6055, 2288, 21292, 3615, 44945, 32887, 5016, 44945, 5172, 2655, 4117, 16247, 10859, 3794, 44945, 3215, 9778, 1211, 2423, 3792, 6055, 2288, 21292, 3615, 15844, 16247, 10859, 3794, 4724, 1829, 9381, 13546, 3792, 6055, 2288, 21292, 3615, 8717, 995, 4587, 9381, 3792, 5551, 25513, 27884, 8978, 18609, 1783, 48817, 16247, 1863, 34105, 4724, 1829, 9381, 13546, 2423, 23565, 9122, 33456, 11296, 39896, 624, 39896, 28423, 3714, 29245, 23328, 3660, 4724, 3794, 20666, 3794, 45340, 7251, 3555, 4587, 7578, 45164, 5551, 9778, 3215, 8315, 624, 6055, 3794, 995, 45865, 23565, 6055, 3555, 4587, 7578, 28423, 6055, 3794, 995, 45865, 8717, 995, 4587, 9381, 18609], 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{"start": 225.23, "end": 225.53, "word": " cos", "probability": 0.5869140625}, {"start": 225.53, "end": 226.43, "word": " أربعة", "probability": 0.6146647135416666}, {"start": 226.43, "end": 226.99, "word": " في", "probability": 0.91552734375}, {"start": 226.99, "end": 227.35, "word": " sine", "probability": 0.4951171875}, {"start": 227.35, "end": 227.61, "word": " X", "probability": 0.366943359375}, {"start": 227.61, "end": 228.01, "word": " DX", "probability": 0.91748046875}, {"start": 228.01, "end": 228.61, "word": " الأن", "probability": 0.791015625}, {"start": 228.61, "end": 228.87, "word": " هنا", "probability": 0.9658203125}, {"start": 228.87, "end": 229.65, "word": " بيصير", "probability": 0.8316650390625}, {"start": 229.65, "end": 229.85, "word": " ال", "probability": 0.94287109375}, {"start": 229.85, "end": 230.17, "word": " cosine", "probability": 0.5}, {"start": 230.17, "end": 230.57, "word": " كأنها", "probability": 0.9484049479166666}, {"start": 230.57, "end": 230.77, "word": " هي", "probability": 0.71142578125}, {"start": 230.77, "end": 231.01, "word": " U", "probability": 0.826171875}, {"start": 231.01, "end": 231.17, "word": " هي", "probability": 0.376708984375}, {"start": 231.17, "end": 231.43, "word": " DU", "probability": 0.40478515625}, {"start": 231.43, "end": 232.01, "word": " موجودة", "probability": 0.990478515625}, {"start": 232.01, "end": 232.21, "word": " بس", "probability": 0.910888671875}, {"start": 232.21, "end": 232.67, "word": " بالسالم", "probability": 0.7229817708333334}, {"start": 232.67, "end": 233.11, "word": " يبقى", "probability": 0.908935546875}, {"start": 233.11, "end": 233.23, "word": " لو", "probability": 0.958984375}, {"start": 233.23, "end": 233.57, "word": " أخدنا", "probability": 0.9530029296875}, {"start": 233.57, "end": 233.93, "word": " U", "probability": 0.95654296875}, {"start": 233.93, "end": 234.29, "word": " تساوي", "probability": 0.8172607421875}, {"start": 234.29, "end": 234.67, "word": " cosine", "probability": 0.52978515625}, {"start": 234.67, "end": 235.01, "word": " تبقى", "probability": 0.9603271484375}, {"start": 235.01, "end": 235.17, "word": " DU", "probability": 0.849609375}, {"start": 235.17, "end": 235.55, "word": " تساوي", "probability": 0.9742431640625}, {"start": 235.55, "end": 235.89, "word": " ناقص", "probability": 0.9921875}, {"start": 235.89, "end": 236.17, "word": " sine", "probability": 0.728515625}], "temperature": 1.0}, {"id": 12, "seek": 26569, "start": 236.55, "end": 265.69, "text": "يعني بدناش احنا نحوّل ل U بدنا نضلنا نستخدمها بدأ الشكل لو حطينا هنا ناقص تبقى هذه كلها هي DU حطينا هنا ناقص من الفترة برا هنا برضه ناقص فعلى طول بنستخدم انه كل واحدة من هدولة U وهذا بيكون هي DU يعني ممكن مباشرة هي كانت أسهل من انه نحوّل ل U لأنها سهلة فهنا في هاي السالب cosine تربيه تكاملها cosine تكيب ع 3 cosine أس 4 تكاملها cosine أس 5 على 5 وفي الآخر بنحط زائد C", "tokens": [40228, 22653, 47525, 8315, 8592, 1975, 5016, 8315, 8717, 5016, 2407, 11703, 1211, 5296, 624, 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