Question

Знайти інтеграл: срочно

Answer 1

Ответ:

$\int\limits (3 {x} ^{2} - 1) ^{7}x dx = \frac{1}{2} \int\limits {(3 {x}^{2} - 1)}^{7} 2xdx = \\ = \frac{1}{2} \int\limits {(3 {x}^{2} - 1) }^{7} d( {x}^{2} ) = \frac{1}{2} \times \frac{1}{3} \int\limits {(3 {x}^{2} - 1)}^{7} d(3 {x}^{2} ) = \\ = \frac{1}{6} \int\limits {(3 {x}^{2} - 1) }^{7} d(3 {x}^{2} - 1) = \\ = \frac{1}{6} \times \frac{ {(3 {x}^{2} - 1)}^{8} }{8} + c = \frac{ {(3 {x}^{2} - 1)}^{8} }{48} + c$