`int tan^3(2t)sec^3(2t) dt` Find the indefinite integral

Expert Answers

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Apply integral substitution: `u=2t`



Take the constant out,


Rewrite the integral as,


Now use the trigonometric identity:`tan^2(x)=sec^2(x)-1`


Again apply the integral substitution:`v=sec(u)`




Apply the sum and power rule,




Substitute back `v=sec(u)` and `u=2t`, and add a constant C to the solution,


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