How do you integrate $int (x+1)sin(x^2+2x+3)$ using substitution?

Question

4344 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-06T10:06:25

$-1/2cos(x^2+2x+3)+C$ .

Le us subst. $x^2+2x+3=t$ , so, $(2x+2)dx=2(x+1)dx=dt$ .

Therefore, $I=int(x+1)sin(x^2+2x+3)dx$

$=1/2int(2x+2)sin (x^2+2x+3)dx=1/2intsint dt=-1/2cost$ .

Hence, $I=-1/2cos(x^2+2x+3)+C$ .

How do you integrate int (x+1)sin(x^2+2x+3)int (x+1)sin(x^2+2x+3) using substitution?