# How to tackle the integral <msubsup> &#x222B;<!-- ∫ --> <mrow class="MJX-TeXAtom-ORD">

nidantasnu 2022-07-02 Answered
How to tackle the integral
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## Answers (1)

cefflid6y
Answered 2022-07-03 Author has 13 answers
Let $t=\mathrm{tan}y$
$\begin{array}{rl}{J}_{n}& ={\int }_{0}^{\frac{\pi }{4}}{\mathrm{sec}}^{2n}y\phantom{\rule{mediummathspace}{0ex}}dy={\int }_{0}^{1}\left({t}^{2}+1{\right)}^{n-1}dt=\sum _{k=0}^{n-1}\frac{\left(\genfrac{}{}{0}{}{n-1}{k}\right)}{2\left(n-k\right)-1}\end{array}$
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