Question

Интеграл (x+1)sin(x^2+2x)

Answer 1

$displaystyle int left(x+1right)sin left(x^2+2xright)dx\ \ u=x^2+2x\ \ int frac{sin left(uright)}{2}du=frac{1}{2}cdot int :sin left(uright)du=frac{1}{2}left(-cos left(uright)right)=frac{1}{2}left(-cos left(x^2+2xright)right)=\ \ =-frac{1}{2}cos left(x^2+2xright)=-frac{1}{2}cos left(x^2+2xright)+C$