Solving a Complicated Integral: Exploring Substitution Method

[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

 

[rocomath]

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

Don't forget your dx.

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

 

[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,

 

[rootX]

yep.

Edit:
http://integrals.wolfram.com/index.jsp?expr=(5*x-x^2)^2/2&random=false
or matlab:
>> syms x;
>> f = (5*x-x^2)^2/2;
>> int(f,x);
>> int(f,x)

ans =

1/10*x^5-5/4*x^4+25/6*x^3

(too lazy to give u the maxima code)

 

[Ocis]

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