# Find the Indefinite Integral part b

• Sep 12th 2010, 12:21 PM
ugkwan
Find the Indefinite Integral part b
Hi again,
Im studying for a exam tomorrow and have another question for this forum =)

⌡ e^(-x) sec^2(e^(-x)) dx

For this problem I approached it by substituting sec^2(e^(-x)) w/ u^2 => I then got stuck w/ (sec^3(e^(-x))/3 * 1/(sec(e^(-x))*tan(e^(-x))) + C

The answer key just gives -tan(e(-x)) + C

• Sep 12th 2010, 12:30 PM
mr fantastic
Quote:

Originally Posted by ugkwan
Hi again,
Im studying for a exam tomorrow and have another question for this forum =)

⌡ e^(-x) sec^2(e^(-x)) dx

For this problem I approached it by substituting sec^2(e^(-x)) w/ u^2 => I then got stuck w/ (sec^3(e^(-x))/3 * 1/(sec(e^(-x))*tan(e^(-x))) + C

The answer key just gives -tan(e(-x)) + C

Substitute $\displaystyle u = e^{-x}$.
Generally speaking, it is not a good idea to try very complicated substitutions "all at once". It would be better to do as mr. fantastic suggests: let $\displaystyle u= e^{-x}$ so that $\displaystyle du= -e^{-x}dx$ and the problem becomes $\displaystyle -\int sec^2(u)du$. Then, perhaps, use another substitution if you found it helpful.