Question

Интеграл замена переменной ​

Answer 1

3.

$\int\limits {e}^{5 {x}^{7} - 1 } {x}^{6} dx \\ \\ 5 {x}^{7} - 1 = t \\ 35 {x}^{6}dx = dt \\ {x}^{6} dx = \frac{1}{35} dt \\ \\ \frac{1}{35} \int\limits {e}^{t} dt = \frac{1}{35} {e}^{t} + C = \frac{1}{35} {e}^{5 {x}^{7} - 1 } + C$

4.

$\int\limits {x}^{9} \cos( {x}^{10} ) dx \\ \\ {x}^{10} dx = dt \\ 10 {x}^{9} dx = dt \\ dx = \frac{}{} \frac{dt}{10} \\ \\ \frac{1}{10} \int\limits \cos(t) dt = \frac{1}{10} \sin(t) +C= \frac{1}{10} \sin( {x}^{10} ) + C$