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Integrate the following and please simplify Tan^3 2x sec 2xdx

Integrate the following and please simplify Tan^3 2x sec 2xdx

Grade:12

1 Answers

Arun
25763 Points
4 years ago
Write tan3(2x) as tan2(2x).tan(2x) = [sec2(2x)-1].tan(2x)

Now the function is :

Integral [sec2(2x)-1] . tan(2x) . sec(2x)dx

​Put sec(2x) = u

sec(2x).tan(2x).dx = du/2

Integral [u2-1]/2

= u3/6 - u/4 + C

= sec3(2x)/6 - sec(2x)/4 + C

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