Предмет: Математика, автор: Али38888

Вычислить интеграл dx/(2x+5)^4 очень нужно помогите.

Ответы

Автор ответа: Alexаndr

$\displaystyle \int\frac{dx}{(2x+5)^4}=\frac{1}{2}\frac{d(2x+5)}{(2x+5)^4}=-\frac{1}{6(2x+5)^3}+C$

Али38888: 6 как получилась

Alexаndr: 1/2 - компенсация, т.к. мы подвели дифференциал под знаменатель(d(2x+5)=2), и еще -1/3 из интеграла степенной функции.

Али38888: Спасибо. Можешь с этим тоже помочь. Найти площадь фигуры ограниченной линиями: y=√x и y=x^3

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