nice-calculus-evaluate-0-pi-2-log-3-tan-x-dx-

Question Number 123255 by mnjuly1970 last updated on 24/Nov/20

* * * n i c e c a l c u l u s * * *

e v a l u a t e ::

Φ = \int_{0}^{\frac{π}{2}} {l o g}^{3} (t a n (x)) d x = ?

Answered by Dwaipayan Shikari last updated on 24/Nov/20

\int_{0}^{\frac{π}{2}} {l o g}^{3} (t a n x) d x = I

= \int_{0}^{\frac{π}{2}} {l o g}^{3} (c o t x) = \int_{0}^{\frac{π}{2}} - {l o g}^{3} (t a n x) = I

2 I = 0 \Rightarrow I = 0

Commented by mnjuly1970 last updated on 24/Nov/20

t h a n k y o u \dots