Question

integral of (1+sinx)/(1-sinx)?
seems like I should separate the integral but that doesn't seem to help much.

Answer 1

multiply and divide with 1+sin(x)
\[\Large \int\limits{}^{} \frac{1+\sin(x)}{1-\sin(x)}*\frac{1+\sin(x)}{1+\sin(x)}\]
\[\int\limits \frac{(1+\sin(x))^2}{1-\sin^2(x)}dx=\int\limits \frac{1+\sin^2(x)+2\sin(x)}{\cos^2(x)}dx\]

Answer 2

ok great thanks

Answer 3

can you complete this or need further help with this ?

Answer 4

Im fine with the other terms but Im having trouble with sin^2/cos^2?

Answer 5

I mean just taking the integral of it.

Answer 6

ok
we can write this by distributing the denominator
\[\int\limits (\frac{1}{\cos^2(x)}+\frac{\sin^2(x)}{\cos^2(x)}+\frac{2\sin(x)}{\cos^2(x)})dx\]
which becomes
\[\int\limits (\sec^2(x)+\tan^2(x)+2\tan(x)\sec(x))dx\]

now seperate the integrals and solve them .
you may know .
\[\int\limits \sec^2(x)dx=\tan(x)\]

Answer 7

yep ok got it thanks again.

Answer 8

you welcome :)