find-dx-tan-1-x-

Question Number 96092 by mhmd last updated on 29/May/20

f i n d \int \frac{d x}{{t a n}^{- 1} (x)}

Commented by bemath last updated on 30/May/20

\int \cot^{- 1} (x) d x = I

by parts . u = \cot^{- 1} (x) \Rightarrow d u = - \sqrt{1 - x^{2}} d x

d v = d x \Rightarrow v = x

I = x \cot^{- 1} (x) + \int x \sqrt{1 - x^{2}} d x

I = x \cot^{- 1} (x) - \frac{1}{2} \int \sqrt{1 - x^{2}} d (1 - x^{2})

I = x \cot^{- 1} (x) - \frac{1}{3} \sqrt{{(1 - x^{2})}^{3}} + c

Commented by Kunal12588 last updated on 30/May/20

\frac{1}{{t a n}^{- 1} x} \neq {c o t}^{- 1} x

[{t a n}^{- 1} (\frac{1}{x}) = {c o t}^{- 1} x]

Commented by mathmax by abdo last updated on 30/May/20

answer not correct!

Commented by MJS last updated on 30/May/20

this cannot be solved

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