1. Jan 25, 2015 #1

   romeIAM

   

   1. The problem statement, all variables and given/known data
   ∫x²(√2+x)
   
   2. Relevant equations
   ∫f(x) from a to b = f'(b) - f'(a)
   and substitution rule
   
   3. The attempt at a solution
   
   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.

    

   romeIAM, Jan 25, 2015
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3. Jan 25, 2015 #2

   Dick

   

   Science Advisor

   Homework Helper

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

    

   Dick, Jan 25, 2015
4. Jan 26, 2015 #3

   Mark44

   

   Insights Author

   Staff: Mentor

   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.

    

   Mark44, Jan 26, 2015
5. Jan 26, 2015 #4

   ehild

   

   Homework Helper

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

    

   ehild, Jan 26, 2015

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