(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int x^{5}\sqrt{x^{2}+1}dx[/tex]

2. Relevant equations

Using various tables for integration.

3. The attempt at a solution

So I want to manipulate it, perhaps get it to look like [itex]\sqrt{a^{2}+u^{2}}[/itex], [itex]\sqrt{a^{2}-u^{2}}[/itex], [itex]\sqrt{u^{2}-a^{2}}[/itex], or maybe even [itex]\sqrt{2au-u^{2}}[/itex]. So I attempt to do some substitutions:

if i let u = x^2, then du = 2x dx and x = sqrt(u)

so i rearrange things and get:

[tex]\frac{1}{2}\int u^{2}\sqrt{u+1}du[/tex]

and while i may (or may not) be able to do this, the question is asking that i use the tables in the back of my textbook, and none of them are given in this form...so...

if i let u = x^4, then in the end, x will equal the cube root of u, which doesn't help at all.

I tried u = x^3, u = x^5, and u = x^2+1 and had no luck...I used wolfram alpha and even it couldn't give me any steps that would help guide me in the right direction.

how do i manipulate this integrand to get something in one of the forms i gave earlier, [itex]\sqrt{a^{2}+u^{2}}[/itex], [itex]\sqrt{a^{2}-u^{2}}[/itex], [itex]\sqrt{u^{2}-a^{2}}[/itex], or [itex]\sqrt{2au-u^{2}}[/itex]. If you can think of any others please let me know.

If not, I guess I just need to let u = x^2 and then substitute. Then after that, we have

[tex]\frac{1}{2}\int u^{2}\sqrt{u+1}du[/tex]

then i guess do integration by parts? even then I'll have a [tex]\int \frac{u^{3}}{\sqrt{u+1}}du[/tex], which isn't part of any tables...

i think i am probably complicating things, but i'm not seeing what technique to use, given that we have to use some sort of table..

thank you in advance for any help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integration using tables

**Physics Forums | Science Articles, Homework Help, Discussion**