Home › AP EAPCET (Engineering) › Mathematics › Integral Calculus › Using partial fractions, 1/(x^2 - a^2) integrate…
Using partial fractions, 1/(x^2 - a^2) integrates to
A(1/a) tan^-1(x/a) + C
B(1/2a) ln|(x - a)/(x + a)| + C
C(1/2a) ln|(x + a)/(x - a)| + C
D(1/2a) ln|(a - x)/(a + x)| + C
Answer & Solution
Correct answer: B. (1/2a) ln|(x - a)/(x + a)| + C
Splitting 1/(x^2 - a^2) into partial fractions gives (1/2a)[1/(x - a) - 1/(x + a)], which integrates to (1/2a) ln|(x - a)/(x + a)|.
Related questions
Differentiating the indefinite integral of f(x) givesBy parts, the integral of u dv/dx dx equalsIntegration by parts follows from which differentiation rule?For A(x) = area function of continuous f, the first fundamental theorem gives A'(x) =Given the velocity at every instant, which process recovers the position?The definite integral of sec^2 x between 0 and pi/4 isGiven that the integral of f from 2 to 5 is 7, the integral of f from 5 to 2 isUsing the property of f(a - x), the integral of sin x/(sin x + cos x) over [0, pi/2] is