1. ## Integration

$\displaystyle integral(16/(xln(4x)dx [e, e^7]$

Can anyone help?

I tried putting it in my calculator and it is unable to work it out.

2. $\displaystyle 16\int_e^{e^7} \frac{{\color{blue}1}}{{\color{blue}x} {\color{red}\ln (4x)}} \ {\color{blue}dx}$

Let: $\displaystyle {\color{red}u = \ln (4x)} \ \Rightarrow \ du = \frac{1}{4x} \cdot 4 \ dx \ \Leftrightarrow \ {\color{blue}du = \frac{1}{x} \ dx}$

Don't forget to change your upper and lower limits.

3. Would a final answer of 20 be correct? If not how do I get the bounds because Im not sure if I did that right.

4. Originally Posted by CalcGeek31
Would a final answer of 20 be correct? If not how do I get the bounds because Im not sure if I did that right.

5. Okay. So to get the new bounds you plug into u right?

so u = ln(4(e)) for the bottom

and u = ln(4(e^7)) for the top?

6. Originally Posted by CalcGeek31
Okay. So to get the new bounds you plug into u right?

so u = ln(4(e)) for the bottom

and u = ln(4(e^7)) for the top?
Correct.