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

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Answer 1 · 2017-01-13T07:13:08

Rewrite as:

#inte^-sin(5x)*cos(5x)dx#

Let #u=-sin(5x)#

#du=-5cos(5x)dx#

#-1/5du=cos(5x)dx#

#-1/5inte^udu#

#=-1/5e^u#

#=-1/5e^-sin(5x)=-e^-sin(5x)/5#