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C4 please help!!!

Ola2898

Use the substitution u^2 = x+1 to evaluate

INT[X^2/√(X+1)]dx

Reply 1

old_engineer

Original post by Ola2898

Use the substitution u^2 = x+1 to evaluate

INT[X^2/√(X+1)]dx

Once you've applied the substitution,

* What does x^2 become?
* What does sqrt(x + 1) become?
* What does dx become?

Reply 2

Ola2898

x^2 = (u^2-1)^2
√(x+1) = u
dx = du/0.5(x+1)^-0.5

Reply 3

old_engineer

Original post by Ola2898

x^2 = (u^2-1)^2
√(x+1) = u
dx = du/0.5(x+1)^-0.5

You will help your cause if you can get dx in terms of u. To do that you can either apply the given substitution to your expression for dx, or alternatively go back to x = u^2 - 1 and find dx/du. The result should be the same.

Then, put it all together and integrate with respect to u.

Reply 4

Roy97

(2/5)u^5-(4/3)u^3+2u
Is it correct??

Original post by Roy97

(2/5)u^5-(4/3)u^3+2u
Is it correct??

I would encourage you to reverse the original substitution to get an expression for the integral in terms of x rather than u. (Hint: take a factor of u outside a new bracket). Then you will be able to differentiate that expression and check that you get back to the original expression.