Question

integrate 9dv/81 - v^4

Answer 1

\[\int\limits_{}^{}9dv/81 - v^4\]

Answer 2

is it integral 9/81 -v^4 dv?

Answer 3

1/9-v^4 dv
1/9v-(v^5)/5+C

Answer 4

\[\int\limits_{}^{}(9dv)/(81 - v^4)\]

Answer 5

Oh !

Answer 6

it uses tanx

Answer 7

http://www.wolframalpha.com/input/?i=integrate+9%2F%2881-v^4%29+dv

Answer 8

it is pretty lengthy

Answer 9

my solutions manual shows \[1/12 \ln|(3+v)/(3-v)| + (1/6) \tan^{-1} (v/3) + C\]

Answer 10

81-v^4 = (9+v^2)(9-v^2)
= (9+v^2)(3+v)(3-v)

Answer 11

id do partial decomps

Answer 12

\[\frac{9}{(81-v^4)}=\frac{Ax+B}{(9+v^2)}+\frac{C}{(3-v)}\frac{D}{(3+v)}\]

Answer 13

Av+B that is

Answer 14

I KNEW IT WAS PARTIAL FRACTIONS!!!!!!

Answer 15

lol .... they do help

Answer 16

yea i was stuck on how i go about breaking it down to irreducible factors though

Answer 17

but i knew it was somewhere with partial fractions thanks

Answer 18

\[\frac{9}{(81-v^4)}=\frac{Av+B}{(9+v^2)}+\frac{C}{(3-v)}+\frac{D}{(3+v)}\]

\[\small 9=Av+B(3-v)(3+v)+C(3+v)(9+v^2)+D(3-v)(9+v^2)\]

Answer 19

for future reference, how do i place numbers over other numbers in the equations tab when i ask a question? Instead of using the / sign.