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

1. ## 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 =)

2. Originally Posted by aa751
Integrate x(f(x))6 dx

I don't know what that "6" means
, using the substitution
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?

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

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

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

3. 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

sorry about the misunderstanding

I actually now understand the 1st and 2nd one but I still dont get the third one

4. For the third one, use trigonometric substitution.

$\displaystyle \int \frac{1}{\sqrt{4-9x^2}}dx$

As HallsofIvy stated, let $3x= 2 \sin(u)$
Therefore $dx = ... du$

Make that substitution then use trigonometric identities to simplify the square root.