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Grade: 12

                        

∫ (tanx) / (a+b tan 2 x) dx , plz answer asap, thank you.

3 years ago

Answers : (1)

Amila Rukshan Senadheera
32 Points
							
First write down the whole fuction using sines and cosines, then you will notice that the you can convert this as
the derivarive of denominator is equal to the numerator. 
I=\int \frac{tan(x)}{a+btan^2(x)} dx = \int \frac{sin(x)cos(x)}{a+(b-a)sin^2(x)} dx
=\frac{1}{2(b-a)}\int\frac{d}{dx} ln|a+(b-a)sin^2(x)|dx = \frac{1}{2(b-a)} ln|a+(b-a)sin^2(x)| + c
 
3 years ago
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