Evaluate the following integrals. \int\sec^{-2}x\tan^3xdx

Kye

Kye

Answered question

2021-10-12

Evaluate the following integrals.
sec2xtan3xdx

Answer & Explanation

cheekabooy

cheekabooy

Skilled2021-10-13Added 83 answers

The given integral is
I=sec2xtan3xdx
We have:
I=sec2xtan3xdx
I=tan3xsec2xdx
I=sin3xcos2xcos3xdx
I=sin3xcosxdx
I=sinxsin2xcosxdx
let cosx=tcos2x=t21sin2x=t2;sin2x=1t2
sinxdx=dt
I=(1t2)tdt
I=(1tt2t)dt
I=(t1t)dt
I=tdt1tdt
( using xndx=xn+1n+1+C and 1xdx=ln|x|+C)
I=t22ln|(t)|+C
I=cos2x2ln|cosx|+C

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