anyone nice @ calc? or at least decent..

[daveyp225]

... since a lot of you are comp sci majors and have taken calculus courses, i'm stuck on an "easy" question.. I have done many others like this and have gotten them correct, but this one after a few trials I have gotten the same wrong answer.. Its just a simple integral problem, and thanks for taking a look, even if ya can't help!

The problem is: (I used the } as the integral symbol)

} x^3 ∙ ( x^4 + 3 )^3 dx

I set ........ u = x^4 + 3
then did..... u' = 4x^3

Since there is a 4 missing from the equation, I multiplied the integral by 1/4:

... 1/4 } (u^3) du

Taking the integral, I get:

... 1/4 ∙ (u^4)/4
... = 1/4 ∙ (x^4 + 3)^4 / 4

final answer...... (x^4 + 3)^4 / 16 + C

What, if anything, did I do wrong? The book's answer is as follows:
(x^4 + 3)^3 / 12 + C

It isn't too different from mine, and that is why if I did make a mistake, I think its going to be something stupid that I will kick myself for..

Thanks a lot! And just so you all know, this is self-help homework, not assigned/graded type stuff.

Dave

[palloco]

the integral of u^3*du is u^3, while you had integrated it twiceas if you were dealing with }}u^3dudu

[discodanman45]

Dave, it looks like you are 100% correct. The book has to be wrong just based that when you integrate x dx you have to end up with a higher order of x. In this case the books solution has a much lower power of x then the original equation. The highest term in the original equation is x^15, the solutions highest term is x^12. That is just nonsense. Your solution looks 100% correct.

By the palloco, your statement is not correct. the integral of u^3*du is 1/4 u^4 just like Dave said.

[daveyp225]

Thanks for the reply, but what I learned was that once the derivitive of the inside function exists (multiplying the integral by 1/4 in this case), the (4x^3)*dx could then be replaced with du, hence (u^3)du.. so "(1/4) } u^3 * du" is the same as "} x^3 ∙ ( x^4 + 3 )^3 dx"..

But in any case, as I stated.. after I found out the problem, i'd be kicking myself.. and I am. I COPIED THE PROBLEM WRONG!

Thanks again!
dave