# Thread: Help me ! integral

1. ## Help me ! integral

1.$\displaystyle \int ln(2x+1)dx$
2.$\displaystyle \int e^{2x}sin3xdx$
3$\displaystyle \int \frac{r^{3}}{\sqrt{4+r^{2}}}dr$

I'm from Vietnam,I can't do it, help me !

2. Originally Posted by butbi9x

1.$\displaystyle \int ln(2x+1)dx$
2.$\displaystyle \int e^{2x}sin3xdx$
3$\displaystyle \int \frac{r^{3}}{\sqrt{4+r^{2}}}dr$

I'm from Vietnam,I can't do it, help me !
Hi

1. You can integrate by parts

$\displaystyle \int ln(2x+1)dx = x ln(2x+1) - \int \frac{2x}{2x+1}dx$

$\displaystyle \int ln(2x+1)dx = x ln(2x+1) - x + \frac{1}{2} ln(2x+1)$

2. Twice by parts

3. By parts with $\displaystyle u'(r) = \frac{r}{\sqrt{4+r^{2}}}$ and v(r)=r²

3. One way to do the third one is to sub $\displaystyle u^2 = 4+r^2$

And just to add on running-gag's advice for number 2, you can treat the integral as the unknown and solve for it.