Partial Fraction Decomposition w/ Trig Functions and Substitution

Hi,

Can someone help me with this problem?

**integral (9sec(theta))/(1+sin(theta))**

WolframAlpha told me to multiply the top and bottom by -cos^2(theta), then converted it into something else using u=sin(theta)... but I don't understand. (I've reached my daily limit of free step-by-step solutions, so it won't let me view it anymore.) Is there another way to do this problem?

Re: Partial Fraction Decomposition w/ Trig Functions and Substitution

I would multiply the integrand in fact by to get:

then use the subsiitution:

to get:

and now use partial fractions to complete the job, back-substituting for at the end.

Re: Partial Fraction Decomposition w/ Trig Functions and Substitution

Now make the substitution and the integral becomes

Now applying Partial Fractions:

Let and we find .

Let and we find

Let and we find . Therefore

Re: Partial Fraction Decomposition w/ Trig Functions and Substitution

Please note that in my hurry to post this I made a few sign errors, I'll fix it when I get the chance. Thanks Mark for pointing them out :)

Re: Partial Fraction Decomposition w/ Trig Functions and Substitution