1. ## stuck finding antiderivative

I'm stuck finding the antiderivative to solve an integral. It's step 6 underlined with a "?".

I think it should be - ( 1/5 * e^5x * cos9x), then we add the C.

2. You're not doing the integration by parts correctly. Your derivative of u is incorrect (you need the chain rule), and your integral of dv is incorrect (use a substitution).

3. make $\displaystyle I = \int e^5x\cos 9x ~dx$

As as you have shown integrating by parts twice is the correct method.

$\displaystyle \int \cos 9x ~dx = \frac{1}{9}\sin 9x$

$\displaystyle \frac{d}{dx}( e^5x)=5e^5x$

4. Isn't d/dx of e^5x = e^4x * 5 ?

Also, I list it as simply du = e^5x dx because my teacher does that for some reason. For instance in the example of e^x he lists it as e^x = e^x dx. So I did the same.. I don't want to learn something the wrong way here I thought my way of showing it was correct.

So if I were to fix this would the rest be ok?

5. Originally Posted by solidstatemath
Isn't d/dx of e^5x = e^4x * 5 ?
Sorry this is not correct.

In general

$\displaystyle \frac{d}{dx}(e^{f(x)})= f'(x)e^{f(x)}$

which you are confusing with $\displaystyle \frac{d}{dx}(x^n)= nx^{n-1}$