`int tan^5(2x)sec^4(2x) dx` Find the indefinite integral

Expert Answers

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Let's apply integral substitution:`u=2x`



Take the constant out and rewrite the integral as,


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


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




apply the sum rule and power rule,




substitute back `v=tan(u)` and  `u=2x`


Add a constant C to the solution,


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