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Mathematics Question on Integration by Partial Fractions

The value of ∫dxx2−6x+13∫\frac{dx}{x^2-6x+13}is:

A

12tan−1x−32+C\frac{1}{2} tan^{-1}\frac{x-3}{2}+C, where C is constant of integration.

B

12cot−1x−32+C\frac{1}{2} cot^{-1}\frac{x-3}{2}+C, where C is constant of integration.

C

12tan−1x+32+C\frac{1}{2} tan^{-1}\frac{x+3}{2}+C, where C is constant of integration.

D

12cot−1x+32+C\frac{1}{2} cot^{-1}\frac{x+3}{2}+C, where C is constant of integration.

Answer

12tan−1x−32+C\frac{1}{2} tan^{-1}\frac{x-3}{2}+C, where C is constant of integration.

Explanation

Solution

The correct option is(A):12tan−1x−32+C\frac{1}{2} tan^{-1}\frac{x-3}{2}+C, where C is constant of integration.