# How do I solve this integral?

1. May 28, 2008

### Ocis

Integrate $$\int$$ $$\frac{\left(5x - x^{2}\right)^{2}}{2}$$

I have been going round in circles using the substitution of u = $$\left(5x - x^{2}\right)$$

But it gets too complicated, where am I going wrong? I would really appreciate it if someone could please explain in stages what exactly I have to do.
Many thanks

Last edited: May 28, 2008
2. May 28, 2008

### rocomath

$$\frac 1 2\int(5x-x^2)^2dx$$

Expand ... $$(x-y)^2=x^2-2xy+y^2$$

Last edited: May 28, 2008
3. May 28, 2008

### Ocis

Is the solution anywhere close to this?

$$\frac{\left(25x ^{3}\right)}{6}$$ $$-$$ $$\frac{\left(10x ^{4}\right)}{4}$$ $$+$$ $$\frac{\left(x ^{5}\right)}{5}$$

Thanks,

4. May 28, 2008

### rootX

Last edited: May 28, 2008
5. May 28, 2008

### Ocis

Oh yeah of course it is, thanks to you all. Panic over!!