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

$$\mathrm{find}\mathrm{the}\mathrm{integration}$$$$\int \sqrt{sin\left(x\right)}dx$$

Answered by smridha last updated on 09/Jun/20

$$\mathit{l}\mathit{e}\mathit{t}..\mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}\right)={\mathit{u}}^2$$$$\mathit{s}\mathit{o}\int 2u^2{(1-{\mathit{u}}^4)}^{-\frac{1}{2}}\mathit{d}\mathit{u}$$$$=2\underset{\mathit{n}=0}{\sum ^{\mathrm{\infty }}}\frac{\left(2\mathbf{n}\right)!}{4^{\mathit{n}}{(\mathit{n}!)}^2}\int {\mathit{u}}^{4\mathit{n}+2}\mathit{d}\mathit{u}$$$$=2\underset{\mathit{n}=0}{\sum ^{\mathrm{\infty }}}\frac{\left(2\mathit{n}\right)!}{4^{\mathit{n}}{(\mathit{n}!)}^2}.\frac{{\left(\mathit{s}\mathit{i}\mathit{n}\mathit{x}\right)}^{\frac{4\mathit{n}+3}{2}}}{(4\mathit{n}+3)}+\mathit{c}$$

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