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.
make $\displaystyle \displaystyle I = \int e^5x\cos 9x ~dx$
As as you have shown integrating by parts twice is the correct method.
Your derivatives need some attention.
$\displaystyle \displaystyle \int \cos 9x ~dx = \frac{1}{9}\sin 9x$
$\displaystyle \displaystyle \frac{d}{dx}( e^5x)=5e^5x$
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?