Substitution Rule for Indefinite Integrals

[temaire]

Homework Statement

$$\int2e^-^7^xdx$$

Homework Equations

None

The Attempt at a Solution

$$(\frac{-2}{7})(\frac{e^-^7^x}{-7})+C$$


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

$$\frac{-2e^-^7^x}{7}+C$$

 

[rocomath]

How did you get two 1/7 terms?

 

[temaire]

I took the antiderivative of $$e^-^7^x$$.

 

[rocomath]

I took the antiderivative of $$e^-^7^x$$.

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]

$$2\int e^{-7x}dx$$

$$-\frac 2 7\int -7e^{-7x}dx$$

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

 

[temaire]

I've got it now, thanks.