Antidifferentiation Question

[allstar]

how would i antidifferentiate [x^4+12x^3+36x^2]^-1?

Moderator Action: Changed topic name from "hello?" to something more relevant.

[keltingmeith]

Factorise the denominator and split it up into partial fractions.

[allstar]

when i factorise i get x^2 (x+6)^2

A(x+6)^2 + Bx^2 = 1

if x = 0 A = 1/36
if x = -6 B = 1/36

so the antidiff is 1/36 integral( 1/x^2 + 1/(x+6)^2)
1/36 [-x^-1 - (x+6)^-1 ]

[keltingmeith]

Just tag on a constant of integration, and it looks fine to me.

[allstar]

thanks

i have a euler's question:

its from the 2011 vcaa exam 2

why did they assume that h is equal to the dy/dx multiplied by t?

[polar1]

thanks

i have a euler's question:

its from the 2011 vcaa exam 2

why did they assume that h is equal to the dy/dx multiplied by t?

I just looked at the examiner's report comment for that question, and they did it the 'standard way'. corresponds to the step size anyway, which, in this case is 1/2.