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## Homework Statement

Hello. I am doing some problems on integration by parts and got stuck on the following problems. Any help would be appreciated.

i. [tex]\int \arcsin x dx[/tex]

ii. [tex]\int_{0}^{1} x \ln (9+x^2) dx[/tex]

iii. [tex]\int x^2 \arctan x\, dx[/tex]

## Homework Equations

[tex]u\,du=uv-v\,du[/tex]

## The Attempt at a Solution

i. I tried u= arcsin x and dv=dx, but ended up with an integral which looks worse than the original question.

ii. I used [itex]u= \ln (9+x^2)\,dx[/itex] but ended up with

[tex]\int_{0}^{1} \frac{x^3}{9+x^2}\,dx[/tex]

which I am stuck with.

iii. I tried u=arctan x and dv= x^2 dx but ended up with a similar looking integral in question ii, which is [tex]\int x \ln(1+x^2)\,dx[/tex]