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Консультация № 109291
13.11.2007, 21:41
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1
Помогите пожалуйста решить задачи по математическому анализу с интеграллами:
1.⌠(2-3e^x)^3 dx;
2.⌠dx/1+16x^2;
3.⌠7dx/3x^3 sqrt(ln x);
1.⌠(2-3e^x)^3 dx;
2.⌠dx/1+16x^2;
3.⌠7dx/3x^3 sqrt(ln x);
Обсуждение
Неизвестный
13.11.2007, 21:53
общий
это ответ
Здравствуйте, Курилов Олег Олегович!
1.
∫(2-3e<sup>x</sup>)³dx = ∫(8-36e<sup>x</sup>+54e<sup>2x</sup>-27e<sup>3x</sup>)dx = 8∫dx – 36∫e<sup>x</sup>dx + 54∫e<sup>2x</sup>dx – 27∫e<sup>3x</sup>dx = 8x – 36e<sup>x</sup> + 27e<sup>2x</sup> - 9e<sup>3x</sup> + C.
2.
∫dx/(1+16x²) = 1/4 * ∫d(4x)/(1+(4x)²) = 1/4 * arctg(4x) + C.
1.
∫(2-3e<sup>x</sup>)³dx = ∫(8-36e<sup>x</sup>+54e<sup>2x</sup>-27e<sup>3x</sup>)dx = 8∫dx – 36∫e<sup>x</sup>dx + 54∫e<sup>2x</sup>dx – 27∫e<sup>3x</sup>dx = 8x – 36e<sup>x</sup> + 27e<sup>2x</sup> - 9e<sup>3x</sup> + C.
2.
∫dx/(1+16x²) = 1/4 * ∫d(4x)/(1+(4x)²) = 1/4 * arctg(4x) + C.
Форма ответа
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