- #1

MelissaJL

- 50

- 0

[itex]\int[/itex][itex]\frac{(6+e^{x})^{2}dx}{e^{x}}[/itex]

I have been having quite some difficulties with this one but here is my work so far:

Let u=e^{x}, du=e^{x}dx

=[itex]\int[/itex][itex]\frac{(u+6)^{2}du}{u^{2}}[/itex]

Then let s=u+6 ∴ u=s-6, ds=du

=[itex]\int[/itex][itex]\frac{s^{2}ds}{(s-6)^{2}}[/itex]

=[itex]\int[/itex][itex]\frac{s^{2}ds}{36-12s+s^{2}}[/itex]

At this point I find myself lost and am not sure what to do. Is there an easier way to solve this integral? Also, if this is the only way to solve it how do I finish it from here? Thank you :)