# Integration by parts?

1. Jan 15, 2006

### johnnyboy2005

integration by parts??

just trying to figure out this integral int(x^2 (1+x^3)^4 dx)

when i integrate by substitution i get anti deriv.... 1/15 (1+x^3)^5

which is not the same (but close when u plug in values of x) to

1/15*x^15 +1/3*x^12 + 2/3*x^9 + 2/3*x^6 + 1/3*x^3

am i going about this wrong?....i'm letting u = 1 + x^3...what

2. Jan 15, 2006

### Tom Mattson

Staff Emeritus
Your answer is right. You must have made a mistake when plugging in values of x.

3. Jan 15, 2006

### fasterthanjoao

bleh, mistake.

4. Jan 15, 2006

### johnnyboy2005

1/15*x^15 +1/3*x^12 + 2/3*x^9 + 2/3*x^6 + 1/3*x^3 is the value i got from maple

1/15 (1+x^3)^5 is the value i got by hand....

plug in values of x....u get different results...

if x=1...

the first one u get 31/15...the second is 32/15

5. Jan 15, 2006

### HallsofIvy

Staff Emeritus
(1/15)(1+ x^3)^5= (1/15)x^15+ (1/3)x^12+ (2/3)x^9+ (2/3)x^6+ (1/3)x^3+ 1/15.

Do the words "constant of integration" mean anything to you?