Homework Help: Substitution Rule for Indefinite Integrals

temaire · May 27, 2008

1. The problem statement, all variables and given/known data
[tex]\int2e^-^7^xdx[/tex]

2. Relevant equations
None

3. The attempt at a solution

[tex](\frac{-2}{7})(\frac{e^-^7^x}{-7})+C[/tex]

This is as far as I can go, but the answer is:

[tex]\frac{-2e^-^7^x}{7}+C[/tex]

rocomath · May 27, 2008

How did you get two 1/7 terms?

temaire · May 27, 2008

I took the antiderivative of [tex]e^-^7^x[/tex].

rocomath · May 27, 2008

temaire said: ↑

I took the antiderivative of [tex]e^-^7^x[/tex].

So, why do you have 1/7 * 1/7? Just do it again from scratch and you'll probably see what you did wrong.

rocomath · May 27, 2008

[tex]2\int e^{-7x}dx[/tex]

[tex]-\frac 2 7\int -7e^{-7x}dx[/tex]

You don't need to divide by another -7. It's already in standard form!

temaire · May 27, 2008

I've got it now, thanks.