Integrate that by parts for integral

[fiziksfun]

i need help taking this integral

[tex]\int[/tex] 9sin[tex]\sqrt{t+1}[/tex]


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

 

[HallsofIvy]

First write it correctly:
[tex]\int 9 sin(\sqrt{t+1}) dt[/tex]

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

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