Evaluate integrate (1/a+bcosx).dx limit 0 to p

put cosx=(1-tan^2(x/2))/(1+tan^(x/2))

integrate sec^2(x/2) dx/a(1+tan^2(x/2)+b(1-tan^2(x/2))

=integrate sec^2(x/2)dx/(a+b)+(a-b)tan^2(x/2)

put tan(x/2)=t

diff w. r. to x we get

sec^2(x/2).1/2 dx=dt

=integrate 2dt/(a+b)+(a-b)t^2

=2/sqrt(a+b) arctan( sqrt(a-b)t/sqrt(a+b))

=2/sqrt(a+b) arctan(sqrt(a-b)tan(x/2)/sqrt(a+b))

Thanks & Regards

Rinkoo Gupta

ASkIITians Faculty

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firstly you just change the cosx into half angel formula than u just put