Integration by substitution and by parts

[barksdalemc]

I did a few problems in integration by parts. There are two that I just can't seem to get. I've tried every type of subsitution or part I can think of.

1. e^sqrt(x)

2. sin (ln x)

 

[arildno]

Rewrite:
1. $$e^{\sqrt{x}}=\frac{2\sqrt{x}}{2\sqrt{x}}e^{\sqrt{x}}$$
2. $$\sin(\ln(x))=\frac{x}{x}\sin(\ln(x))$$
On 2., you'll get an integration "cycle"

 

[courtrigrad]

Or let $$u = e^{\sqrt{x}}$$ and $$dv = dx$$