How do I compute the following integral \(\displaystyle{I}=\int{\left({\tan{{x}}}\right)}^{{\frac{{1}}{{6}}}}{\left.{d}{x}\right.}\)

Deegan Chase

Deegan Chase

Answered question

2022-03-27

How do I compute the following integral
I=(tanx)16dx

Answer & Explanation

Roy Brady

Roy Brady

Beginner2022-03-28Added 19 answers

First use the substitution tanx=u and then use another substitution u=t6 to get
I=(tanx)16dx
=u161+u2du
=5t61+t12dt
=5t61+t12dt
For tackling down the last integral you should use partial fractions. You may wonder that the denominator has no real roots. The answer is that the partial fraction decomposition works for complex roots as well.

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