Answer :

in this integral we will use the formula 1+tan2x=sec2x,

Then equation will be transform in below form-


I = ∫tan3x sec2x sec2x dx


= ∫tan3x (1 + tan2x) sec2x dx


Now put tanx=t which means sec2xdx=dt,




Now put the value of t,which is t=tanx in above integral-



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