What is the difference between integrating by substitution and by parts?

[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

 

[quantumdude]

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

 

[fasterthanjoao]

bleh, mistake.

 

[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

 

[HallsofIvy]

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

(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?