# Can't evaluate the Integral

∫x2(√2+x)

## Homework Equations

∫f(x) from a to b = f'(b) - f'(a)
and substitution rule

## The Attempt at a Solution

[/B]
I decided to make u=√(2+x), du= 1/2√(2+x) and when solving dx, i got dx= 2√(2+x) du. Substituting and then simplifying, I managed to get ∫2(x^2)u^2 du. But i can't go further from there. i can't find a way to get rid of the x2, I didn't get far using u= x2 or u=x+2 so I'm pretty sure i'm using the right substitution. I need help.

Dick
Homework Helper

∫x2(√2+x)

## Homework Equations

∫f(x) from a to b = f'(b) - f'(a)
and substitution rule

## The Attempt at a Solution

[/B]
I decided to make u=√(2+x), du= 1/2√(2+x) and when solving dx, i got dx= 2√(2+x) du. Substituting and then simplifying, I managed to get ∫2(x^2)u^2 du. But i can't go further from there. i can't find a way to get rid of the x2, I didn't get far using u= x2 or u=x+2 so I'm pretty sure i'm using the right substitution. I need help.

Try making u=2+x. Then x=u-2. So x^2=(u-2)^2. Take it from there.

Mark44
Mentor
I managed to get ∫2(x^2)u^2 du.
When you do a substitution, do a complete substitution. In this case, neither x nor dx should appear after you make the substitution.

Also, in your original integral, you omitted dx. It's not a good habit to get into to ignore the differential. Doing so will come back to bite you in other integration techniques, including trig substitution and integration by parts.

ehild
Homework Helper

∫x2(√2+x)

## The Attempt at a Solution

[/B]
I decided to make u=√(2+x), du= 1/2√(2+x) here. i can't find a way to get rid of the x2, I didn't get far using u= x2 or u=x+2 so I'm pretty sure i'm using the right substitution. I need help.

No need to substitute. Just expand the integrand, and integrate the sum by terms.