# Math Help - Integral and quick simplification problems

1. ## 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:

i thought that the answer should be :
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:

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

2. 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:

i thought that the answer should be :
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:

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

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

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

The integral can easily be written in the form $\int\frac{f'(x)}{f(x)}dx=\ln(f(x)) +C$. Do you see how to do this? The derivative of the denominator is $6e^{6x}$.
So you should write $\int\frac{e^{6x}}{5+e^6x}dx=\frac{1}{6}\int\frac{6 e^{6x}}{5+e^{6x}}dx$.
Then use the formula to obtain $\frac{1}{6}\ln(5+e^{6x}) +C$