Question

find the general antiderivative of f(x)=(e^(sinx))(cosx)

Answer 1

Let u = sinx, du = cosxdx
Then,\[\int\limits e^udu = e^uu \prime\]

Answer 2

What is the mark after the u?

Answer 3

To calculate
\[\int e^{\sin x}\cos x dx\]
Make u = sin x, and du = cos x dx

Answer 4

Then:
\[\int e^u du=e^u+\text{constant}\]

Answer 5

So your answer should be
\[e^{\sin x}+\text{constant}\]
The constant is important, because the question is asking for the general antiderivative.