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Integration by Substitution

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  • #1
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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:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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You are on the right track, but I would check that du again.
 
  • #3
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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)
 
  • #4
48
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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
 
  • #5
33,182
4,860
You put the dx in this time. That's a good habit to get into, especially when you start doing trig substitutions.
 
  • #6
48
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Thanks Mark44
 

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