# Integration by parts

1. Mar 22, 2012

### Roodles01

knowing the standard form for integration by parts is
∫ f(x)g'(x) dx = f(x)g(x) - ∫f'(x)g(x) dx

I have what is an innocuous looking part of an equation which I can't solve.

the f(x) part in this case is;
ln(5x) which is easy enough i.e. 1/x

the second part 1/(x(2/3)) is the bit I can't solve.

The standard I have for
1/x is ln(x)+c
& the standard I have for xn is (1/(n+1))xn+1+c

But these don't solve this for me

I have checked on WolframAlpha & NumberEmpire & they give the same answer
3 cuberoot 3

I have tried just this bit by itself & go t nowhere. Could someone help with how I should get 3 cuberoot 3, please.

2. Mar 22, 2012

### Dick

1/x^(2/3)=x^(-2/3). So put n=(-2/3) into x^(n+1)/(n+1).

3. Mar 22, 2012

### Roodles01

I'm being thick here, but doesn't (n+1)/(n+1) = 1

So x1 = x ?

Sorry.

Last edited: Mar 22, 2012
4. Mar 22, 2012

### Dick

Ok, I'll be a little clearer. I meant the formula you referred to $\frac{x^{n+1}}{n+1}$.

5. Mar 22, 2012

### HallsofIvy

Staff Emeritus
Yes, it is true that x1= x! However, the anti-derivative of x1 is x1+1/(1+1)= x2/2.

I am surprised that you are being asked to use "integration by parts" but do not know how to integrate xn.

6. Mar 22, 2012

### Roodles01

I shall try to be more numerically erudite in future!

I think that sometimes I have to ask stupid questions when I have come to the end of my tether & I can't see the wood for the trees.

Practice makes perfect & asking stupid questions should embarrass me into remembering it properly.

Prepare for more along the same lines in the future.

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