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Evaluate: int1/(sin^2x+sin2x)dx...

Evaluate: `int1/(sin^2x+sin2x)dx`

Text Solution

Verified by Experts

I=`int1/(sin^2x+sin2x)dx`
I=`int(sec^2xdx)/(tan^2x+2tanx)`
let`tanx=t`,`sec^2xdx=dt`
I=`int(sec^2xdx)/(tan^2x+2tanx)`
=`int dt/(t^2+2t)`
=`1/2int (1/t-1/(t+2))dt`
=`1/2[ln(t)−ln(t+2)]+C`
=`1/2[ln(tanx)−ln(tanx+2)]+C`
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