Evaluate the following integrals. inttan^3 4x dx

defazajx 2021-01-23 Answered
Evaluate the following integrals.
tan34x dx
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Expert Answer

broliY
Answered 2021-01-24 Author has 97 answers
To evaluate:
tan34x dx
tan2x=sec2x1
ddx(secx)=secxtanx
Considertan34xdx
=tan24xtan4xdx
=(sec24x1)tan4xdx
Now, let sec4x=u
4sec4xtan4xdx=du
tan4xdx=du4sec4x
Substituting all the values, we get,
(u21)dusec4x
=(u21)du4u
=14u21udu
=14u1udu
=14[u22ln(u)]+C
=14[sec24x2ln(sec4x)]+C
Hence, tan34x dx=14[sec24x2ln(sec4x)]+C
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