Solv Indefinite Integral: x^3/sqrt[1 + x^2] dx

JimmyCat
Messages
1
Reaction score
0
I'm having a problem with the following integral: x^3/sqrt[1 + x^2] dx

Can this be done with substitution or integration by parts?
Throw me some hints at this one please!

Sorry I forgot to include my attempt.

I tried solving this by substitution, letting u=1-x^2. Then letting (-1/2)du = xdx. Simplifying it down and came to the answer of 1/3(1-x^2)-sqrt(1-x^2) + C
 
Last edited:
Physics news on Phys.org
Please make an attempt at the solution, or this thread will be deleted.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top