Question

What did I do wrong? Please see image
http://i1084.photobucket.com/albums/j409/QRAWarrior/WTH-MATA30Y-Wrong.png

Answer 1

That is the question clearly stated, and the answer along with it.

Answer 2

But what did I do wrong?

Answer 3

first off, you can't take e^2 out of the integrand like that...

Answer 4

notice that the bottom factors and is quadratic in e^x, so factor it

Answer 5

You did a couple of things wrong.
good start: let u= e^x and du = e^x dx so dx= du/u
notice that
\( e^{2x}= e^x \cdot e^x \) or \( (e^x)^2 =u^2\)
note that \( e^2\cdot e^x= e^{x+2} \) is not what you want.

using the substitution the problem is
\[ \frac{1}{u}\frac{3u^2}{u^2+13u+40} du = \frac{3u}{u^2+13u+40} du\]

Now you can use partial fraction expansion to finish off the problem