# Integration, general power formula

• May 3rd 2013, 10:59 AM
togo
Integration, general power formula
Question - integrate the following:

(int) (4- (e^x))^3 e^x dx

attempt:
u = (4 + e^x)
n = 3
du = e^x

((4 + (e^x))^4) / 4 + c

which is incorrect, and should be:
4 / (e^(x^1/2)) + c

Stared at it for a while and can't figure it out. Any help, thanks?
• May 3rd 2013, 11:09 AM
Plato
Re: Integration, general power formula
Quote:

Originally Posted by togo
Question - integrate the following:

(int) (4- (e^x))^3 e^x dx

attempt:
u = (4 + e^x)
n = 3
du = e^x

((4 + (e^x))^4) / 4 + c

which is incorrect, and should be:
4 / (e^(x^1/2)) + c, NO indeed!

$\displaystyle \int {{{\left( {4 - {e^x}} \right)}^3}{e^x}dx = - \tfrac{1}{4}} {\left( {4 - {e^x}} \right)^4} + c$
• May 3rd 2013, 11:14 AM
mathguy25
Re: Integration, general power formula
Need to find $\displaystyle \int (4 - e^x)^3 e^x dx$.

Set $\displaystyle u = 4 - e^x$. Then $\displaystyle du = -e^x dx$. Then $\displaystyle -du = e^x dx$

$\displaystyle \int (4 - e^x)^3 e^x dx = \int -u^3 du = -\frac{u^4}{4} + C = -\frac{(4 - e^x)^4}{4} + C$
• May 3rd 2013, 01:35 PM
togo
Re: Integration, general power formula
you guys are telling me the book is wrong
• May 3rd 2013, 01:41 PM
Shakarri
Re: Integration, general power formula
Try differentiating the book's answer to check that it is correct