Question

integration of 5tanx/(tanx-2)
how do i approach this?

Answer 1

\(5 \int\limits \frac{ \tan(x) }{ \tan(x)-2 }dx\) Is this correct?

Answer 2

Yep.

Answer 3

You COULD convert: \(tan(x)= \frac{ \sin(x) }{ \cos(x) }\) and try and simplify.

Answer 4

Doesnt help i guess. Unless you can come up with something.
sinx/(sinx-2cosx) dx is what i get.

Answer 5

it is simple
put tan(x)-2=u
and simplify

Answer 6

Ok so sec^2x dx=du
what i get is (t+2)/(sec^2x*t) dt.. what next @irshadno1 ?

Answer 7

1 + tan^2x = sec^2

Answer 8

Yeah i got it.
What we have to do is, put tanx=t, solve put sec^2=1+t^2... use partial fractions and simplify. I was forgetting to use partial fractions.
You were the closest.
Thank you.