1. Jun 22, 2010

### pinnacleprouk

Could you please confirm my answers as correct or incorrect, if incorrect please point out errors and assist in correcting errors.

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

Intergrate the following functions with respect to x using recognition, substitution or intergration by parts:

x^2(2+x^3)^4

x(x^2+2)^5

xcosx

3. The attempt at a solution

1)
integral(x^2(2+x^3)^4)
put (2+x^3) =x
thus
3x^2dx = dz
or
x^2dx = dz/3

the integral becomes
integral(z^4dz)/3
= z^5/15
=(2+x^3)^5/15 + c

2)
integral(x(x^2+2)^5)
put x^2+2=z
or
2xdx = dz
thus
xdx = dz/2
integral(z^5/2)dz
= z^6/12+c
=(x^2+2)^6/12 + c

3) integral(xcosx)
x(sinx) - integral(sinx)
= -xsinx+cosx +c

2. Jun 22, 2010

### Susanne217

You can test your final result using either mathematical software like Maple, Mathematica and or google Wolfram integrator it using the integration engine of Mathematica.

3. Jun 22, 2010

### pinnacleprouk

while I appreciate your reply, I would rather ask here to see if the steps taken are correct as well as the final result!

Thanks

4. Jun 22, 2010

### DJsTeLF

I think you mean (2+x^3) = z

Last one is definitely correct and, albeit a little tedious, the other 2 can easily be confirmed by expanding the brackets and integrating directly.

5. Jun 22, 2010

### Susanne217

Okay, but as you know which I learned yesterday its forbidden to reply with re-calculations to you.

2) and 3) are correct but you need to redo 1) using integration by parts and integration by substitution!