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How do you integrate #(e^sin(x))cos(x) dx#?

Answer 1

Cameron Alexander

#inte^(sinx)cosxdx=e^sinx#

Let #u=sinx#, then #du=cosxdx# and

#inte^(sinx)cosxdx=inte^udu=e^u=e^sinx#

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Answer 2

William Abdalla

To integrate ( (e^{\sin(x)})\cos(x) ) with respect to ( x ), you can use integration by parts. Let ( u = e^{\sin(x)} ) and ( dv = \cos(x) dx ). Then, differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ). Finally, apply the integration by parts formula: [ \int u , dv = uv - \int v , du ]. After evaluating the integral, you will obtain the result.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.