Integration using Table of Integrals

[spyke200]

Here's the problem I'm struggling with. It should be fairly simple and straightforward as it is one of the first questions in my homework (but yet... )

Integrate x^2 / sqrt [9 + (4x)^2]

The way i see it is this is an 'sqrt(a^2 + u^2)' which is sqrt [3^2 + (2x)^2]. However with this problem we have an 'a' and a 'b' but the 'a' does not match with the x^2 (...on the numerator). My question is am i doing it wrong or is there something I am missing.

 

[Deleted member 4993]

Here's the problem I'm struggling with. It should be fairly simple and straightforward as it is one of the first questions in my homework (but yet... )

Integrate x^2 / sqrt [9 + (4x)^2]

The way i see it is this is an 'sqrt(a^2 + u^2)' which is sqrt [3^2 + (2x)^2]. However with this problem we have an 'a' and a 'b' but the 'a' does not match with the x^2 (...on the numerator). My question is am i doing it wrong or is there something I am missing.

This is not a simple look-up-in-the-table problem.

substitute:

4x = 3 * tan(Θ)

 

[spyke200]

This is not a simple look-up-in-the-table problem.

substitute:

4x = 3 * tan(Θ)

I started out with what you said, but then i got a little stuck. (see attachment #1) Using what you said, and what i can remember I subsituted x = 3/2 * tan(Θ) instead and this is what I got. (see attachment #2)

If i go on one more step I will get something like this: (see attachment #3) where basically all that's remaining is to integrate and distribute. I am fairly new to using the table, as you've probably noticed, so I just need to know if I am on the right track or if there is a mistake I am overlooking somewhere.

 

[Yogi]

This is not a simple look-up-in-the-table problem. You sure?

I think you are overworking yourself, if the directions say look it up on a table then you could use something like the following:
http://integral-table.com/
Go down to #36
Let u=4x to start and convert back to x at the end.

 

[HallsofIvy]

Here's the problem I'm struggling with. It should be fairly simple and straightforward as it is one of the first questions in my homework (but yet... )

Integrate x^2 / sqrt [9 + (4x)^2]

The way i see it is this is an 'sqrt(a^2 + u^2)' which is sqrt [3^2 + (2x)^2].

No, it isn't, unless you have written this incorrectly. It is (4x)^2 not (2x^2)- unless your original problem was
sqrt[9+ 4x^2].

However with this problem we have an 'a' and a 'b' but the 'a' does not match with the x^2 (...on the numerator). My question is am i doing it wrong or is there something I am missing.

It's simple algebra. Assuming you initially meant "4x^2" rather than "(4x)^2", this would be \(\displaystyle x^2= (1/4)(4x^2)\) and you can take the "1/4", a constant, outside the integral:
\(\displaystyle \int \frac{x^2}{\sqrt{9+ 4x^2}}dx = \frac{1/4}\int \frac{4x^2}{\sqrt{9+ 4x^2}}dx= \frac{1}{4}\int \frac{(2x)^2}{\sqrt{3^2+ (2x)^2}}dx\)