Integration by Parts: Solve y(1+y^2)^1/2 dy

Thread starter Song
Start date Nov 10, 2006
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Integration Integration by parts parts

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The integral y(1+y^2)^(1/2) dy can be approached using u-substitution, where u = 1 + y^2 and du = 2y dy, leading to a solution of (1/3)(1+y^2)^(3/2). Some participants suggest that integration by parts could also be used by expanding the expression and setting u as y. Trigonometric substitution, particularly using tan, is mentioned as an alternative method due to the presence of y^2 in the integral. Overall, u-substitution is highlighted as the most straightforward approach to solve the integral effectively.

Nov 10, 2006

Song

integral y(1+y^2)^1/2 dy

can someone help me with this?

Thanks.

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Nov 10, 2006

Song

trigonometirc sub.

Nov 10, 2006

Bernie Hunt

Wouldn't this solve easier with u substituion?
u = 1+y^2
du = 2y dy

Solution is 1/3(1+y^2)^3/2

If you want integration by parts, multiply it out and make u to be y so that du is 1.

By trig you'll need to substitute tan because the problem is + Y^2.

Bernie

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