# Different techniques of integration

1. Sep 29, 2004

### DennisG

hi, we're working on different techniques of integration and I just wanted to know if I got the right answer for this...

$$\int\frac{x^3}{(x+1)^10} dx$$ (the denominator should be raised to the tenth and not the 1 with a big zero after it, if someone could tell me how to raise it to a power like that, it would also be appreciated)

I only got $$\frac{-(x+1)^-11}{11}\times\frac{x^4}{4}$$

thanks

Last edited: Sep 29, 2004
2. Sep 29, 2004

### faust9

First, I'll address the latex problem: x^{10} will display $x^{10}$. Superscripting and subscripting should be surrounded by {}.

Next, what new method are you using? You can use the tabular method (a relative of integration by parts) and I'm sure there's at least one more method.

Another thing, if you have a graphing calculator you can check your answer by evaluating the indefinate integral as a definate integral--say 0 to 1 in this case. Evaluate your answer as a definate and see if the numbers you get from both methods are the same... I evaluated the original int from 0 to 1 and got a positive number and I see the bottom will yield a negativeover the same limits, so your answer is wrong. If you show us what you've done then someone will be able to point out your mistake.

Anyway, good luck.

3. Sep 29, 2004

### Pyrrhus

DennisG

Try this

$$u = x+1$$

so

$$(u-1)^3 = x^3$$

Do you see it now?

4. Sep 29, 2004

ohhhhhh
thanks a lot