U-Substitution for Indefinite Integrals

[01010011]

Hi, am I on the right track with this U-substitution problem?

Homework Statement

Evaluate the indefinite integral

Homework Equations

integral of x^2(x^3 + 5)^9 dx

The Attempt at a Solution

integral of x^2(x^3 + 5)^9 dx

Let u = x^3 + 5

du = 2x^2

1/2du = x^2

1/2 integral u^9 du

1/2 (u^10)/10 + c

1/20 u^10 + c

1/20 (x^3 + 5)^10 + c

 

[Dick]

You are on the right track, but I would check that du again.

 

[Lunat1c]

Let u = x^3 + 5

du = 2x^2

This is where you're wrong. Just a slight mistake,

Remember that the differentiation of x^n is n*x^(n-1)

 

[01010011]

You are on the right track, but I would check that du again.

This is where you're wrong. Just a slight mistake,

Remember that the differentiation of x^n is n*x^(n-1)

Thanks for your replies Dick and Lunat1c. I see the mistake, i'll try it again:

The Attempt at a Solution

integral of x^2(x^3 + 5)^9 dx

Let u = x^3 + 5

du = 3x^2 dx

1/3du = x^2 dx

1/3 integral u^9 du

1/3 (u^10)/10 + c

1/30 (u^10) + c

1/30 (x^3 + 5)^10 + c

 

[Mark44]

You put the dx in this time. That's a good habit to get into, especially when you start doing trig substitutions.

 

[01010011]

Thanks Mark44