find-dx-arcsinx-1-x-2-

Question Number 36752 by prof Abdo imad last updated on 05/Jun/18

f i n d \int \frac{d x}{a r c s i n x \sqrt{1 - x^{2}}} .

Commented by tanmay.chaudhury50@gmail.com last updated on 05/Jun/18

i s i t \int \frac{d x}{{s i n}^{- 1} (x \sqrt{1 - x^{2}})} p l s c l a r i f y

Commented by abdo.msup.com last updated on 05/Jun/18

f i n d \int \frac{d x}{\sqrt{1 - x^{2}} a r c s i n (x)}

Commented by tanmay.chaudhury50@gmail.com last updated on 05/Jun/18

o k \dots s i r

Commented by prof Abdo imad last updated on 06/Jun/18

c h a n g e m e n t x = s i n θ g i v e

I = \int \frac{c o s θ d θ}{θ c o s θ} = \int \frac{d θ}{θ} = l n ∣ θ ∣ + c

I = l n ∣ a r c s i n (x) ∣ + c .

Answered by tanmay.chaudhury50@gmail.com last updated on 05/Jun/18

\int \frac{d x}{(\sqrt{1 - x^{2}}) {s i n}^{- 1} x}

t = {s i n}^{- 1} x

x = s i n t

d x = c o s t d t

\int \frac{c o s t d t}{\sqrt{1 - {s i n}^{2} t} \times t}

\int \frac{d t}{t} = l n t + c

= l n ∣ ({s i n}^{- 1} x) ∣ + c