Integral and quick simplification problems

• Jan 26th 2010, 05:57 PM
jason0
Integral and quick simplification problems
Hi guys, I've been struggling with these two problems and was wondering if anyone could give me some help to get going in the right direction, thanks in advance

the first problem is:

Find the indefinite integral:
http://i47.tinypic.com/35aj9u0.jpg

i thought that the answer should be :
http://i49.tinypic.com/mc8caw.jpg plus C but that's not correct, I'm not sure how else to do this problem

the second problem is:

Write the expression as a logarithm of a single quantity:
http://i50.tinypic.com/2qklel0.jpg

not sure how to get started on this one, I know the laws of logarithms, I'm mainly confused on what to do with the 1/2 and the 5
• Jan 26th 2010, 06:09 PM
Quote:

Originally Posted by jason0
Hi guys, I've been struggling with these two problems and was wondering if anyone could give me some help to get going in the right direction, thanks in advance

the first problem is:

Find the indefinite integral:
http://i47.tinypic.com/35aj9u0.jpg

i thought that the answer should be :
http://i49.tinypic.com/mc8caw.jpg plus C but that's not correct, I'm not sure how else to do this problem

the second problem is:

Write the expression as a logarithm of a single quantity:
http://i50.tinypic.com/2qklel0.jpg

not sure how to get started on this one, I know the laws of logarithms, I'm mainly confused on what to do with the 1/2 and the 5

The integral can easily be written in the form $\displaystyle \int\frac{f'(x)}{f(x)}dx=\ln(f(x)) +C$. Do you see how to do this? The derivative of the denominator is $\displaystyle 6e^{6x}$.

So you should write $\displaystyle \int\frac{e^{6x}}{5+e^6x}dx=\frac{1}{6}\int\frac{6 e^{6x}}{5+e^{6x}}dx$.

Then use the formula to obtain $\displaystyle \frac{1}{6}\ln(5+e^{6x}) +C$
• Jan 26th 2010, 06:16 PM
jason0
Quote:

Originally Posted by adkinsjr
The integral can easily be written in the form $\displaystyle \int\frac{f'(x)}{f(x)}dx=\ln(f(x)) +C$. Do you see how to do this? The derivative of the denominator is $\displaystyle 6e^{6x}$.

So you should write $\displaystyle \int\frac{e^{6x}}{5+e^6x}dx=\frac{1}{6}\int\frac{6 e^{6x}}{5+e^{6x}}dx$.

Then use the formula to obtain $\displaystyle \frac{1}{6}\ln(5+e^{6x}) +C$

got it, thanks so much