Integrate that by parts for integral

[fiziksfun]

i need help taking this integral

$$\int$$ 9sin$$\sqrt{t+1}$$


help please! i don't even know where to start :[

 

[HallsofIvy]

First write it correctly:
$$\int 9 sin(\sqrt{t+1}) dt$$

Make the obvious substitution $u= \sqrt{t+1}= (t+1)^{1/2}$ so that $du= (1/2)(t+1)^{-1/2}dt$ or 2udu= dt.
(Equivalently, u²= t+ 1.)

That changes your integral to
$$9\int u sin(u)du$$
and you can integrate that by parts.