Integral of exponential function

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$\int \left(\cos10x\right) \; e^{\sin10x} \; dx$

**Answer**

$\int \left(\cos10x\right) \; e^{\sin10x} \; dx$

Substitute $u= \sin10x$. So, $du =10\cos10x\; dx$

And, $\frac{1}{10}\; du = \cos 10x\; dx$

Then $\int \left(\cos10x\right)\;e^{\sin10x} \; dx$

$=\frac{1}{10}\int e^{u} \; du$

$=\frac{1}{10}e^u + C $

Substituting back $u= \sin 10x$

$=\frac{1}{10}e^{\sin 10x} + C$