How do you integrate $\int \frac{cos (5 x)}{e^{sin (5 x)}}$ $int cos(5x)/e^(sin(5x))$ using substitution?

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Answer 1 · 2017-01-13T07:13:08

Rewrite as:

$\int e^{- sin (5 x)} \cdot cos (5 x) d x$ $inte^-sin(5x)*cos(5x)dx$

Let $u = - sin (5 x)$ $u=-sin(5x)$

$d u = - 5 cos (5 x) d x$ $du=-5cos(5x)dx$

$- \frac{1}{5} d u = cos (5 x) d x$ $-1/5du=cos(5x)dx$

$- \frac{1}{5} \int e^{u} d u$ $-1/5inte^udu$

$= - \frac{1}{5} e^{u}$ $=-1/5e^u$

$= - \frac{1}{5} e^{- sin (5 x)} = - \frac{e^{- sin (5 x)}}{5}$ $=-1/5e^-sin(5x)=-e^-sin(5x)/5$

How do you integrate int cos(5x)/e^(sin(5x))∫cos(5x)esin(5x)int cos(5x)/e^(sin(5x)) using substitution?