Evaluate the integral ∫ [x^3/sqrt(x^2+1)] in two different ways.

a) Integration by parts

b) The substitution u = sqrt(x^2+1)

Not sure how to do this, help would be greatly appreciated!

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- May 17th 2011, 11:41 PMbrumby_3Evaluating an integral
**Evaluate the integral ∫ [x^3/sqrt(x^2+1)] in two different ways.**

a) Integration by parts

b) The substitution u = sqrt(x^2+1)

Not sure how to do this, help would be greatly appreciated!

- May 18th 2011, 12:36 AMchisigma
a) by parts...

... taking into account the identity...

http://quicklatex.com/cache3/ql_f8ed...4a24645_l3.png (1)

... is...

http://quicklatex.com/cache3/ql_0e65...8fda6c7_l3.png

http://quicklatex.com/cache3/ql_37da...292da11_l3.png (2)

Kind regards

- May 18th 2011, 12:55 AMTheCoffeeMachine