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Question Number 123551 by joki last updated on 26/Nov/20

Answered by ebi last updated on 26/Nov/20

$$I=\int cosx{(1+sinx)}^{4}dx$$$$letu=1+sinx$$$$\frac{du}{dx}=cosx\Rightarrow dx=\frac{du}{cosx}du$$$$I=\int u^{4}du=\frac{u^5}{5}+c=\frac{{(1+sinx)}^5}{5}+c$$

Commented by joki last updated on 26/Nov/20

$$thankyousir$$

Answered by Olaf last updated on 26/Nov/20

$$\mathrm{F}\left(x\right)=\int \cos x{(1+\sin x)}^{4}dx$$$$\mathrm{F}\left(x\right)=-\frac{1}{5}{(1+\sin x)}^5+\mathrm{C}$$$$\left(\mathrm{trivial}\right)$$

Commented by joki last updated on 26/Nov/20

$$thankyousir$$

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