Evaluate the integral. \int\sec^3x\tan^4x dx

Dolly Robinson 2021-10-20 Answered
Evaluate the integral.
sec3xtan4xdx
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tabuordg
Answered 2021-10-21 Author has 99 answers
The given integral is:
I=sec3xtan4xdx
=sec3x(tan2x)2dx
=sec3x(sec2x1)2dx
=sec3x(sec4x2sec2x+1)dx
=sec7xdx2sec5xdx+sec3xdx
Solving each of the component integrals we get,
I=ln(tanx+secx)16+sec5xtanx67sec3xtanx24+secxtanx16+C
where C is the constant of integration.
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