Math Is Fun Forum

fangree01

Member

Registered: 2006-11-13

Posts: 11

Integration - Change of Variable

Hi there,

I hate to be a pain with the change of variable questions but  I have no solutions for the worksheet we were given so I have no idea if I am doing them right so your help is very much appreciated.

The question is ∫x dx/x^4 + 9

My answer is 1/3 tan-¹ x²/3 and I am very unsure of this.

I would be grateful for any help.

Thanks

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Integration - Change of Variable

Whats the derivative of 1/3 tan-¹ x²/3

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Integration - Change of Variable

Use the substitution u = x[sup]2[/sup].

As I said to someone else in http://www.mathsisfun.com/forum/viewtopic.php?id=7261:

Checking integration answers is very easy – just differentiate your answer and see if you get the original expression back.

fangree01

Member

Registered: 2006-11-13

Posts: 11

Re: Integration - Change of Variable

Hi,

Thanks for all your help.