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Integration

the integral of 3 / (x^2(x+2) = 3/4( ln(x + 2 /2) -2/x) + c , prove

so ive split it into a partial fraction

3 = a(x + 2) + b(x)(x + 2) + c(x^2)

so a= 2/3 , b =-3/4, c=3/4

so integral of 2/3x -3/4x^2 +3/4(x+2)

take 3/4 out as a factor so intregal of 2/x - x^-2 + 1/(x + 2)

where do i go from here?

is this correct?
3/4 [ 2lnx + ln(x+2) -1/x]


FIGURED IT OUT
(edited 7 years ago)
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Avatar for B_9710
B_9710
18
From what I can make out it seems you're doing the partial fractions wrong.
You should have 3x2(x+2)≡Ax+Bx2+Cx+2 \displaystyle \frac{3}{x^2(x+2)}\equiv \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x+2} .

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