1. ## A Integration problem..:S

Hallo to all, i have a problem with calculating a integral, i tried it with substitution and partial integration, but had no luck. Please help if someone have an idea. Thank you!
The result is one of the following:
a) 1
b) 2
c) ln 2
d) 1/4 *ln 5
4) 1/2 * ln 3

(the problem is described in the picture)

2. The bounds for the integral in the picture are incorrect - are you sure that's the correct problem?

3. Integration by parts works for me. Use $\mbox{Ei} (-x) =\int_{-\infty}^x \dfrac{e^{-x}}{x}\, dx$

Edit
Ei is the exponential integral

4. i tought also that it is incorrect but it was written so in my college exam.

5. This is what I get.

$\int_0^x \dfrac{e^{-x}\sin^2 x}{x}\, dx=\dfrac{1}{2}\mbox{Ei}(-x)-\dfrac{1}{4}\mbox{Ei}(-(1+2i)x)-\dfrac{1}{4}\mbox{Ei}((-1+2i)x)+\dfrac{1}{4}\ln 5$