- #1
charbon
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Homework Statement
Integrate x^3sqrt(x^2+4)
The attempt at a solution
I have no idea how to substitute this integral in my favor. Can someone please set me on the right track? Thanks
charbon said:I'm sorry but I'm really clueless.
What step in my substitution did I do wrong?
Your work is correct - it's mine that is in error. Sorry for giving bad advice.charbon said:I'm sorry but I'm really clueless.
What step in my substitution did I do wrong?
charbon said:Thank you both very much. The answer they give is [1/15(x^2+4)^3/2](3x^2-8) + c
The formula for integrating x^3sqrt(x^2+4) is ∫x^3√(x^2+4) dx = (√(x^2+4) * (x^2+2)) / 5 + C
To solve an integral with a radical in the integrand, you can use the substitution method by letting u = x^2 + 4 and du = 2x dx. This will transform the integral into a simpler form that can be solved using basic integration rules.
Yes, the integral of x^3sqrt(x^2+4) can be solved using integration by parts. However, it may result in a more complex form and may require multiple applications of the integration by parts formula.
No, there is no specific range of values for x in which the integral of x^3sqrt(x^2+4) can be solved. The integral can be solved for any value of x as long as the integrand is continuous over the given interval.
There are several methods for solving the integral of x^3sqrt(x^2+4) including substitution, integration by parts, and partial fraction decomposition. The most suitable method may vary depending on the complexity of the integrand and the given interval.