Evaluate the indefinite integral.

Question

Can you solve this Calculus problem for me. I just can't understand it at the moment. Evaluate the indefinite integral. Integrate by part?

Integral e^x cos x dx

Answer 1

Step 1:

The integral is .

Apply integration by parts : .

Consider and .

Substitute the values of in .

.

Step 2:

Now solve for .

Apply integration by parts : .

Consider and .

Substitute the values of in .

.

Step 3:

Substitute in the integral expression of .

Add to each side.

Solution :

.