What is the integral of x*sin(sqrt.(x^2 + 4))/sqrt.(x^2 + 4) ?

1 Answer
Jun 19, 2018

I=cos(x2+4)+C

Explanation:

We want to integrate

I=xsin(x2+4)x2+4dx

Make a substitution u=x2+4du=2xdx

I=xsin(u)u12xdu

I=12sin(u)udu

Make a substitution s=uds=12sdu

I=12sin(s)s2sds

I=sin(s)ds

I=cos(s)+C

Substitute back s=u and u=x2+4

I=cos(x2+4)+C