Question

queria a resolucao passo a passo da integral por substituicao de (2x^2+2x-3)^10(2x+1)dx

Answer 1

$\int {(2x^2+2x-3)^{10}(2x + 1)} \, dx$

u = 2x² + 2x - 3
du = (4x + 2 ) dx = 2 (2x + 1) dx

$\int {(u)^{10}(2x + 1)} \, \frac{du}{2(2x+1)}$

$\int {(u)^{10}} \, \frac{du}{2}$

$\int {\frac{(u)^{10}}{2}} \, du$

$\frac{(u)^{11}}{2*11}+C$

$\frac{(u)^{11}}{22}+C$

$\frac{(2x^2+2x-3)^{11}}{22}+C$