Question

Перовообразная от 5x^3/√(7x-2x^4)

Answer 1

Ответ:

$\int\limits \frac{5 {x}^{3}dx }{ \sqrt{7 - 2 {x}^{4} } } \\ \\ 7 - 2 {x}^{4} = t \\ - 16 {x}^{3} dx = dt \\ {x}^{3} dx = - \frac{dt}{16} \\ \\ - \frac{1}{16} \int\limits \frac{dt}{ \sqrt{t} } = - \frac{1}{16} \int\limits {t}^{ - \frac{1}{2} } dt = \\ = - \frac{1}{16} \times \frac{ {t}^{ \frac{1}{2} } }{ \frac{1}{2} } + C = - \frac{1}{8} \sqrt{t} + C= \\ = - \frac{1}{8} \sqrt{7 - 2 {x}^{4} } + C$