Integral of exponential function

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$\int \sin34x\;e^{{\cos}^217x} \; dx$

**Answer**

$\int \sin34x\;e^{{\cos}^217x} \; dx$

Substitute $u= {\cos}^217x$

So, $du =-34\sin17x\;\cos17x\; dx$

Or, $du =-17\sin34x\; dx$

And, $-\frac{1}{17}\; du = \sin34x\; dx$

Then $\int \sin34x\;e^{{\cos}^217x} \; dx$

$=-\frac{1}{17}\int e^{u} \; du$

$=-\frac{1}{17}e^u + C $

Substituting back $u= {\cos}^217x$

$=-\frac{1}{17}e^{{\cos}^2 17x} + C$