find-the-integration-sin-x-dx-

Question Number 97590 by bhuvanmahant last updated on 08/Jun/20

find the integration

\int \sqrt{s i n (x)} d x

Answered by smridha last updated on 09/Jun/20

l e t . . s i n (x) = u^{2}

s o \int 2 u^{2} {(1 - u^{4})}^{- \frac{1}{2}} d u

= 2 \underset{n = 0}{\sum^{\infty}} \frac{(2 n)!}{4^{n} {(n!)}^{2}} \int u^{4 n + 2} d u

= 2 \underset{n = 0}{\sum^{\infty}} \frac{(2 n)!}{4^{n} {(n!)}^{2}} . \frac{{(s i n x)}^{\frac{4 n + 3}{2}}}{(4 n + 3)} + c

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