How do you integrate e^(sinx) cosx dx?

2 Answers
Dec 19, 2016

e^(sin(x))+C

Explanation:

You can solve the integral using a u-substitution

Let u=sin(x)

Differentiating we get

du=cos(x)dx

Make the subtitution

int e^udu

integrating we get e^u

Now back substitute for u

e^(sin(x))+C

Dec 19, 2016

if you recognise the result
" "d/(dx)(e^f(x))=f'(x)e^((f(x))" "

you can integrate this directly.

Explanation:

" "d/(dx)(e^sinx)=cosxe^(sinx)" "

so intcosxe^(sinx)dx" "=e^sinx+C