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Question Number 68046 by mhmd last updated on 03/Sep/19

Answered by mind is power last updated on 03/Sep/19

$$\frac{d\left(e^{\frac{sin\left(2x\right)}{2}}\right)}{dx}=cos\left(2x\right)e^{sin\left(x\right)cos\left(x\right)}$$$$\int \frac{e^{sin\left(x\right)cos\left(x\right)}cos\left(2x\right)}{1+e^{sin\left(2x\right)}}dx$$$$=\int \frac{d\left(e^{\frac{sin\left(2x\right)}{2}}\right)}{1+e^{2\frac{sin\left(2x\right)}{2}}}=\int \frac{d\left(e^{\frac{sin\left(2x\right)}{2}}\right)}{1+{\left(e^{\frac{sin\left(2x\right)}{2}}\right)}^2}={\tan }^{-1}\left(e^{\frac{sin\left(2x\right)}{2}}\right)+c$$

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