Math Is Fun Forum

boneill3

Member

Registered: 2008-08-17

Posts: 3

Integration by substitution

Hi Guys,
Im working on an integration problem using substitution and wondering if I'm doing it right.
Can some one please Have a look and see how i'm going?

The problem is int x sqrt 3*x+8

first I let u = 3*x + 8  which makes du/dx = 3

I than integrate  int   sqrt u     = int u^1/2

= 1/3 int 2/3 (u^3/2) + C

=1/3 (2/3(3*x+8)^3/2 + C)

Is this right?
regards
Brendan

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integration by substitution

Just to make sure I've got this right, I think you're doing

.
If that's the case, then your method is perfect.

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Integration by substitution

The problem is int x sqrt 3*x+8

Isn't that

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integration by substitution

I thought so at first, but the method doesn't match up to it. I assumed the first x was saying what to integrate with respect to, since the dx is missing as well.

Boneill, if you were trying to do Ricky's version, then you'd need to involve integration by parts as well as the substitution that you did.

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It wanted to be normal.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Integration by substitution

no it wouldn't mathsy, it can be done with plain substitution using the same substitution:

Last edited by luca-deltodesco (2008-08-18 05:35:31)

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boneill3

Member

Registered: 2008-08-17

Posts: 3

Re: Integration by substitution

Hi Guys Thankyou for your replies.
Do you always solve for X if the derivative of the inner function (3x + 8 ) is not the exactly the first function ie x
once again thank you.
regards
Brendan