Integrate (x)/(x^2-3)^2 = ...
A. (1)/2(x^2-3)+C
B. (1)/(x^2-3)+C
C. (2)/(x^2-3)+C
D. -((1)/(x^2-3))+C
E. -((1)/2(x^2-3)+C
A. (1)/2(x^2-3)+C
B. (1)/(x^2-3)+C
C. (2)/(x^2-3)+C
D. -((1)/(x^2-3))+C
E. -((1)/2(x^2-3)+C
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= ∫(x)/(x^2 - 3)^2 d(x^2 - 3)/2x
= ∫1/(2(x^2 - 3)^2) d(x^2 - 3)
= (1/2)∫(x^2 - 3)^(-2) d(x^2 - 3)
= (1/2)(-(x^2 - 3)^(-1)) + C
= -1/(2(x^2 - 3)) + C
= E.