Question

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(u) =( u^4 + 8 sqrt(u))/(u2)

Answer 1

Have you tried anything yet? I'd recommend starting with simplifying(or re-writing) the 2nd term so you aren't dealing with a fraction.

Answer 2

i have and came up with this u^2+(8sqrut(u))/(u^2)+C and its wrong

Answer 3

so you came up with 8u^(-3/2) when simplifying the 2nd term?

Answer 4

no what i posted was my answer i did most of it in my head

Answer 5

Okay, well, do you remember how to divide exponents that have the same base (like in your 2nd term)?

Answer 6

i dp

Answer 7

do*

Answer 8

ok, good. so before we even try to integrate I would simplify that 2nd term. Unless I made a mistake, it is what I wrote above.

Answer 9

ok let me see

Answer 10

k i got it

Answer 11

great. now we should be able to use the basic rules of integration. for that first term, what does it become when we integrate it?

Answer 12

1/3u^3-16u^(-1/2)+C is the answer

Answer 13

oh, lol, I didn't even see that u^2 was under everything. so that first term becomes just u^2 after simplyfing. after that, yeah I agree, we just apply n+1 to the exponents and also divide by n+1.

Answer 14

yeah i got it right its we assaign

Answer 15

nice. and it makes sense now?

Answer 16

indeed it does thanks