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# C3 Integration by Parts Q watch

1. Hey,

Can anyone show me the working for integral of x*(1+x)^1/2 using integration by parts and also using substitution u= 1+x? I can't seem to get the right answer :/
2. (Original post by couruthim)
Hey,

Can anyone show me the working for integral of x*(1+x)^1/2 using integration by parts and also using substitution u= 1+x? I can't seem to get the right answer :/
What have you tried?
3. I tried by parts, here's my working:
u= x, v=2/3(x+1)^3/2
du/dx= 1, dv/dx= (x+1)^1/2

2/3x(x+1)^3/2 - integral of 2/3(x+1)^3/2
=2/3x(x+1)^3/2- 4/15(x+1)^5/2 + c
4. (Original post by couruthim)
I tried by parts, here's my working:
u= x, v=2/3(x+1)^3/2
du/dx= 1, dv/dx= (x+1)^1/2

2/3x(x+1)^3/2 - integral of 2/3(x+1)^3/2
=2/3x(x+1)^3/2- 4/15(x+1)^5/2 + c
You can simplify it a little to get the result that Wolfram gives.
5. (Original post by joostan)
You can simplify it a little to get the result that Wolfram gives.
Ok, the simplification is the bit I don't get then, how can it be simplified to give the answer on Wolfram?
6. (Original post by couruthim)
Ok, the simplification is the bit I don't get then, how can it be simplified to give the answer on Wolfram?
Pull out a factor of: .
Then simplify what remains in the usual way. It's a linear term so it's reasonably easy to rearrange into the desired form.

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