# Homework Help: Tricky Integration

1. Dec 5, 2017

### squenshl

1. The problem statement, all variables and given/known data
How do I solve $\frac{20\ln{(t)}}{t}$???

2. Relevant equations

3. The attempt at a solution
Is it easier to calculate this without integrating by parts???
I'm not sure where to start.

2. Dec 5, 2017

### andrewkirk

Solving by integration by parts is easy - very few lines. I can't think of an easier way.

3. Dec 5, 2017

### Tallus Bryne

There is an easier way. Try a simple "u-substitution".

4. Dec 5, 2017

### Staff: Mentor

You have $f\cdot f'$ which is half of $(f^2)'$. Done.

5. Dec 5, 2017

### Tallus Bryne

I like the simplicity, but shouldn't it be just half of $(f^2)$ ?

edited: forgot the "half of"

6. Dec 5, 2017

### Staff: Mentor

$f^2$ is the solution after integration, but I said $f \cdot f' = \frac{1}{2} \cdot (f^2)'$ for the integrand. Of course this all is a bit sloppy: no integration boundaries or the constant, no mentioning of $\ln |x|$ in the OP and no $dt 's$.

7. Dec 5, 2017

### Tallus Bryne

Agreed. Thanks for clearing that up.

8. Dec 6, 2017

### Math_QED

Substitute $u = \ln t, du = \frac {1}{t}dt$

9. Dec 6, 2017

### squenshl

Thanks everyone. The solution is $10\ln{(t)}^2$.

10. Dec 7, 2017

### SammyS

Staff Emeritus
You might like to remove an ambiguity.

Is that the natural log of the square of t, or is it the square of the natural log of t ?

Also, I suspect that you need to include a constant of integration .

11. Dec 7, 2017

### MidgetDwarf

Typically for integrals involving ln in a typical calculus course...

Always try u sub. If that does not work, then integration by parts. Keep this in mind.