Mathematics

$$\displaystyle\int e^{\sin x}\cdot\left(\begin{matrix} \dfrac{sin x+1}{sec x}\end{matrix}\right)dx$$ is equal to?


ANSWER

$$\sin x\cdot e^{\sin x}+c$$


SOLUTION
$$\displaystyle\int e^{\sin x}(\sin x\cos x+\cos x)dx$$

We know $$\displaystyle\int e^{g(x)}(g'(x)f(x)+f'(x))dx=e^{g(x)}\cdot f(x)+c$$

Here $$f(x)=g(x)=\sin x$$ and $$f'(x)=g'(x)=\cos x$$

$$=e^{\sin x}\cdot \sin x+c$$.
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Single Correct Medium Published on 17th 09, 2020
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