is this expression correct?

Question

∫e^cosxdx=e^-sinx+C

 

 

Answer 1

We can either integrate the left side, or we can derive the right side.  Let's take the derivative of the right side.  We should get back the left side.

 

 

Using the chain rule

 

-cosx(e^-sinx) ≠ e^cosx

 

 

We did not get back the term on the left side, the expression is not correct.