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

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SUMMARY

The integral of x^3/sqrt[1 + x^2] dx can be effectively solved using substitution. The user attempted substitution with u=1-x^2, leading to an expression of 1/3(1-x^2)-sqrt(1-x^2) + C. However, a more suitable substitution would be u = 1 + x^2, which simplifies the integral more efficiently. This discussion emphasizes the importance of choosing the right substitution for solving integrals.

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JimmyCat
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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
 
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