# Integration by Substitution

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

Last edited:

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

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)

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

Thanks Mark44