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 :/
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?
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
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
I agree with your answer, and so does Wolfram.
You can simplify it a little to get the result that Wolfram gives.
Original post by joostan
I agree with your answer, and so does Wolfram.
You can simplify it a little to get the result that Wolfram gives.
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?
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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