Question

∫▒〖(x+1)(x^2 〗+2x+5)^12 dx

não consegui resolver esta integral

Answer 1

Oi. Espero que ajude em algo:

$\int {[(x+1)(x^2)]+(2x+5)^{12}} \, dx \\ \\ \int {[x^3+x^2]+(2x+5)^{12}} \, dx \\ \\ \int {x^3} \, dx+\int {x^2} \, dx+\int {(2x+5)^{12}} \, dx \ \ \ u=2x+5 \ \ \ du=2.dx\\ \\ \frac{x^{3+1}}{3+1}+ \frac{x^{2+1}}{2+1}+ \frac{1}{2} \int {u^{12}} \, du \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{1}{2} \frac{u^{12+1}}{12+1} +C \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{1}{2} \frac{u^{13}}{13} +C \\ \\ \frac{x^{4}}{4}+ \frac{x^{3}}{3}+ \frac{(2x+5)^{13}}{26} +C$