# Integration questions

1. Oct 23, 2008

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

I'm wondering if anyone can check these integrations for me, or suggest alternative answers if they're not quite right, or can be simplified?

1) $$\int x^{\sqrt{2}}$$

2) $$\int x . \sqrt{x}$$

3) $$\int \frac{1}{x^\pi}$$

2. Relevant equations

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3. The attempt at a solution

1) $$\int x^{1.4} = \frac{x^{2.4}}{2.4} + C$$

2) $$\int x . x^{\frac{1}{2}} = \frac{x^2}{2} . \frac{x^{\frac{3}{2}}}{\frac{3}{2}} = \frac{x^{\frac{3}{2}}}{3} . x^2 + C$$

3) $$\int \frac{1}{x^\pi} = \int x^{-\pi} = \frac{x^{-\pi+1}}{-\pi+1} + C$$

2. Oct 23, 2008

### Vuldoraq

The first and the third look okay to me, although in the first one I would leave the $$\sqrt{2}$$ rather than putting 2.4.

In the second your almost there. When doing this sort of integral it is often easier if you simplify the integrand. By combining $$x*\sqrt{x}$$ into $$\sqrt{x*x^2}$$ to get $${x^{3/2}}$$ it should be easier to integrate.

3. Oct 23, 2008

### HallsofIvy

Staff Emeritus
$\sqrt{2}$ is NOT equal to 1.4! There is no reason to change $x^{\sqrt{2}}$ to $x^{1.4}$.

An unfortunately common mistake: just as you cannot differentiate a product by just differentiating each part, you cannot integrate a product that way either. As Vuldoraq said, $x\sqrt{x}= x(x^{1/2})= x^{3/2}$. Integrate that.

Yes, this is correct.

4. Oct 23, 2008

Thanks for the replies Vuldoraq, HallsofIvy.

So, my answer should be $$\int x^{\frac{3}{2}} = \frac{2x^{\frac{3}{2}}}{3}$$

5. Oct 23, 2008

### SunGod87

You forgot to increase the exponent by one before dividing!

6. Oct 23, 2008

### dirk_mec1

Are you aware of the fact that you're leaving out the dx in the integrals?

7. Oct 23, 2008

alright..

Second attempt.

$$\int x^{\frac{3}{2}} = \frac{2x^{\frac{5}{2}}}{5}$$

8. Oct 23, 2008

### Vuldoraq

Thats it, much better.

To repeat what HallsofIvy said: you can't integrate products of the function being integrated in the usual manner. So you have to simplify and when you can't simplify you have to use a different method (like integration by parts or substitution, you'll come accross these later on).