# Integration help please these are three small even basic integration problems

• Nov 2nd 2010, 10:46 AM
aa751
Integration help please these are three small even basic integration problems
Integrate x(f(x))6 dx, using the substitution u = f(x).( where f(x) is 9x^2 -4

Integrate x+2/f(x) dx where f(x) is 9x^2 -4

Integrate 1/(4-9x^2)^1/2 dx

Please a step by step process is appreciated as I am horrible in integration and need help, Thank you for your help =)
• Nov 2nd 2010, 01:35 PM
HallsofIvy
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Originally Posted by aa751
Integrate x(f(x))6 dx

I don't know what that "6" means
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, using the substitution
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u = f(x).( where f(x) is 9x^2 -4
You are told= what to do- DO IT! Let u= 9x^2- 4. What is du?

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Integrate x+2/f(x) dx where f(x) is 9x^2 -4
Is this $\displaystyle x+ \frac{2}{f(x)}$ or $\displaystyle \frac{x+ 2}{f(x)}$?

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Integrate 1/(4-9x^2)^1/2 dx
Think of "$\displaystyle \sqrt{1- sin^2(x)}= cos(x)$". Try 3x= 2sin(u).

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Please a step by step process is appreciated as I am horrible in integration and need help, Thank you for your help =)

• Nov 2nd 2010, 11:45 PM
aa751
x(f(x))^6 dx thats what I meant sorry
the second question is actually Integrate (x+2)/f(x) sx where f(x)= 9x^2-4

$\displaystyle \displaystyle \int \frac{1}{\sqrt{4-9x^2}}dx$
As HallsofIvy stated, let $\displaystyle 3x= 2 \sin(u)$
Therefore $\displaystyle dx = ... du$