# Antiderivative math homework help

1. Apr 14, 2010

### Nope

1. The problem statement, all variables and given/known data

$$\int(2x^2+1)^7$$

2. Relevant equations

3. The attempt at a solution
u=2x^2+1
du=4xdx
u7 (1/4x)du
I am stuck... I don't know what to do next...

2. Apr 14, 2010

### Staff: Mentor

Re: Antiderivative

Try to remember to put in the differential...
Substitution won't work in this case, which you already found out. If you expand $\int(2x^2+1)^7$, you'll get a polynomial that you can integrate pretty easily.

3. Apr 14, 2010

### Nope

Re: Antiderivative

wow, so i have to expand everything out? (2x^2+1)^7
that's a lot
is there any other way to do it?

4. Apr 14, 2010

### vela

Staff Emeritus
Re: Antiderivative

The x2 suggests a trig substitution might work.

Edit: Actually, that looks to be more of a pain than just multiplying the polynomial out.

Hint: Use the binomial theorem.

5. Apr 14, 2010

### Staff: Mentor

Re: Antiderivative

Nope, I don't think so, at least no way that's not a lot more complicated.

6. Apr 14, 2010

### elect_eng

Re: Antiderivative

Is using a symbolic processor cheating? From Maxima ...

ratsimp((2*x^2+1)^7);

$$128\,{x}^{14}+448\,{x}^{12}+672\,{x}^{10}+560\,{x}^{8}+280\,{x}^{6}+84\,{x}^{4}+14\,{x}^{2}+1$$

7. Apr 14, 2010

### Staff: Mentor

Re: Antiderivative

Probably not, but will you have one available during a test?

8. Apr 14, 2010

### Nope

Re: Antiderivative

No , I don't think so.

9. Apr 15, 2010

### HallsofIvy

Staff Emeritus
Re: Antiderivative

It does help to know the "binomial theorem":

$$(a+ b)^n= \sum_{i=0}^n \begin{pmatrix}n \\ i\end{pmatrix}a^{i}b^{n-i}$$