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

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SUMMARY

The integral of y(1+y^2)^(1/2) dy can be effectively solved using u-substitution, where u = 1+y^2 and du = 2y dy. The solution to the integral is confirmed as (1/3)(1+y^2)^(3/2). While integration by parts is an alternative method, it requires additional steps such as multiplying out the expression and setting u to y, which simplifies the process. Trigonometric substitution is also suggested, specifically using tan, due to the presence of the y^2 term.

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

can someone help me with this?

Thanks.
 
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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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