Integration Problem: Check My Work for (cos(x)/(7*sin(x)+21)) Solution

[Aerosion]

Homework Statement

(integrate)((cos(x)/(7*sin(x)+21))

Homework Equations

The Attempt at a Solution

I actually solved it, but I fear it might be wrong (that and my calculator says a different answer).

Anyway, I factored a 1/7 out of the equation, to make the equation (1/7)(integrate)((cos(x)/(sin(x)+21)). I subsituted (sin(x)+21) for u, and made du cos(x).

This made the integral (1/u), which I turned into ln(u). Now I had (1/7)*ln(u). I just rewrote that into ln(u)/7, then subbed sin(x)+21 into u, making the answer ln(sin(x)+21)/7.

Did I do anything wrong here?

 

[ziad1985]

if i understood what you wrote it should be like this after factoring the 1/7
(1/7)(integrate)((cos(x)/(sin(x)+3))

 

[HallsofIvy]

Yes. The denominator is 7sin(x)+ 21= 7(sin(x)+ 3).