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Can't evaluate the Integral

  • Thread starter romeIAM
  • Start date
  • #1
8
1

Homework Statement


∫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.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618

Homework Statement


∫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.
 
  • #3
33,285
4,989
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.
 
  • #4
ehild
Homework Helper
15,427
1,827

Homework Statement


∫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.
 

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