Question

whats the integral of 1/ ( x * (3-x) )
I know it should be a ln ( something)

Answer 1

do u know hw to use partial fractions?

Answer 2

\[\frac{1}{x(3-x)} = \frac{A}{x}+\frac{B}{3-x}\]

Answer 3

\[1=A(3-x)+bx\]\[1=3A-Ax+Bx\]\[3A=1\]\[A=\frac{1}{3}\]\[-A+B=0\]\[\frac{-1}{3}+B=0\]so\[B=\frac{1}{3}\]

Answer 4

\[\frac{1}{x(3-x)}=\frac{1}{3x} + \frac{1}{3(3-x)}\]

Answer 5

Thanks i can integrate that.

Answer 6

:)