# Homework Help: Help solving a fraction integral

1. Sep 25, 2008

### protivakid

1. The problem statement, all variables and given/known data

$$\int$$(5sin xcosxdx)/(2+52sinx)

3. The attempt at a solution

I set u = sinx and du = cosxdx which gives me...

$$\int$$(5udu)/(2+52u). I just need a little push as where to go from here, not the entire solution, just a push as what to do next. I have a feeling I need to use ln and know that ar = r ln(a) but don't know if I am supposed to use that on the 5u or not, any help is appreciated. Thanks in advance. :)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 25, 2008

### sutupidmath

U could take this subs, at the very beginning

$$\int\frac{5^{sin(x)}cosxdx}{2+(5^{sinx})^2}$$ so taking another substitution here will work quite nicely..

$$5^{sinx}=\sqrt2 u=>\sqrt2 du=5^{sinx}cos(x)ln(5)dx$$ now i guess you know how things turn out to be, right?

3. Sep 25, 2008

### protivakid

That helped a lot, would the final answer then be (1/ln(5)$$\sqrt{}2$$)tan-1(5sinx/$$\sqrt{}2$$) ? The only thing I was not sure about was the ln(5) as far as how to deal with that.

4. Sep 26, 2008

### sutupidmath

take the derivative of your final answer and see if you get the integrand, then its okay, cuz i won't bother to do the whole thing. The general format of it looks okay, but i didn't check the details.

5. Sep 26, 2008

### HallsofIvy

52u= (5u)2 so the next step would be the substitution v= 5u, dv= ln(5) 5udu.