# Homework Help: Antiderivative and Indefinite Integration

1. Mar 5, 2013

### domyy

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

∫(x3 - 3x2 + x + 1)/√x dx

3. The attempt at a solution

∫x3-1/2 - 3∫x2-1/2 + ∫x1-1/2 + ∫x1-1/2

∫x5/2 - 3∫x3/2 + ∫x1/2 + ∫1/2

(x7/2)7/2 - (3x5/2)5/2 + (x3/2)3/2 + (x3/2)3/2 + C

(2x7/2)/7 - (6x5/2)/5 + 2x3/2)/3 + (2x3/2)/3 + C

Thank you so much!!

2. Mar 5, 2013

### MostlyHarmless

First, the last integral you wrote, should be $$∫{\frac{1}{√x}}$$
Second, When integrating, you divide by the new power, you are multiplying, so you should 2/7, 2/5.. etc..

Edit: Im not sure what you did on the line jsut after integrating, but the line after it is mostly right, except for that last part.

3. Mar 5, 2013

### domyy

I don't know if I understand it.

If I have:

∫x3/√x dx

= ∫x3 - 1/2
= ∫x5/2
= (x5/2 + 1)/ 5/2 +1
= (x7/2)/7/2 + C

Simplyfying:

2x7/2/7 + C

Is this correct?

If not, what am I doing wrong?

Also, I am not sure how to proceed with ∫1/√x dx

If I have ∫1 dx:

= 1 + C

So for ∫1/√x dx I'll have:

=x/√x
=x . x- 1/2
=x1/2
=(x1/2+ 1)/1/2 +1 + C

4. Mar 5, 2013

### MostlyHarmless

The first part was right. for ∫1/√x dx. rewrite it as ∫x-1/2dx

EDIT: Nowhere in the equation would you have ∫1dx, but if you did. it would be x+c, not 1+c.