Integration with Natural Logs

**Chinnie15** · December 8th 2010, 01:46 PM

I am having issues with some problems with the integration of natural logs/substitution. I was fine at the beginning of the chapter, but now I'm having some problems. These are a few examples of the type I'm stuck on:

1) The integral of (1/(1+2x^(1/2))dx

2) The integral of (cot(theta/3))d-theta

For the first I tried substitution and got u=1+2x^(1/2), but the du is what is confusing me. I'm just not sure how to proceed.

And the second one I realize you change cot into cos/sin, but I'm confused as to why in the answer a 1/3 (and a 3 to counteract it) is added to the integral? I'm just confused with the process...

If anyone could kindly guide me in the right direction, I would be forever thankful!

Last quiz of the semester is tomorrow morning and I really want to do well on it!

**pickslides** · December 8th 2010, 01:57 PM

Originally Posted by Chinnie15

1) The integral of (1/(1+2x^(1/2))dx

Is this $\displaystyle\int \frac{1}{\sqrt{1+2x}} ~dx$ or $\displaystyle\int \frac{1}{1+\sqrt{2x}} ~dx$ ??

**Chinnie15** · December 8th 2010, 01:59 PM

The second one.

Sorry about that.

**skeeter** · December 8th 2010, 02:07 PM

Originally Posted by Chinnie15

I am having issues with some problems with the integration of natural logs/substitution. I was fine at the beginning of the chapter, but now I'm having some problems. These are a few examples of the type I'm stuck on:

1) The integral of (1/(1+2x^(1/2))dx

2) The integral of (cot(theta/3))d-theta

For the first I tried substitution and got u=1+2x^(1/2), but the du is what is confusing me. I'm just not sure how to proceed.

And the second one I realize you change cot into cos/sin, but I'm confused as to why in the answer a 1/3 (and a 3 to counteract it) is added to the integral? I'm just confused with the process...

If anyone could kindly guide me in the right direction, I would be forever thankful!

Last quiz of the semester is tomorrow morning and I really want to do well on it!

$\displaystyle 1) u = 1 + 2\sqrt{x}<br />$

$\displaystyle du = \frac{1}{\sqrt{x}} dx$

$\displaystyle dx = \sqrt{x} \, du<br />$

$\displaystyle dx = \frac{u-1}{2} \, du$

$\displaystyle \int \frac{1}{1+2\sqrt{x}} \, dx$

substitute ...

$\displaystyle \int \frac{1}{u} \cdot \frac{u-1}{2} \, du<br />$

$\displaystyle \frac{1}{2} \int 1 - \frac{1}{u} \, du$

integrate and back substitute.

2) $\displaystyle \int \frac{\cos\left(\frac{t}{3}\right)}{\sin\left(\fra c{t}{3}\right)} \, dt$

$\displaystyle u = \sin\left(\frac{t}{3}\right)$

$\displaystyle du = \frac{1}{3} \cos\left(\frac{t}{3}\right) \, dt$

$\displaystyle 3 \int \frac{1}{3} \cdot \frac{\cos\left(\frac{t}{3}\right)}{\sin\left(\fra c{t}{3}\right)} \, dt$

substitute ...

$\displaystyle 3 \int \frac{du}{u}$

integrate and back substitute.

**Chinnie15** · December 8th 2010, 02:45 PM

I've got it now, thanks!

Thread: Integration with Natural Logs

LinkBack

Thread Tools

Display

Integration with Natural Logs

Similar Math Help Forum Discussions

Few HW problems involving Logs, Natural logs, and Continuity.

Natural Logs help

[SOLVED] Integration and natural logs

Dealing with Logs and Natural Logs

several questions-logs/natural logs

Search Tags