allery∫ dx/(a² - x²) (for |x| < a):
Aarcsin(x/a) + C
B(1/2a) ln |(a+x)/(a-x)| + C
C-arctan(x/a) + C
Dln |a-x| + C
Answer & Solution
Correct answer: B. (1/2a) ln |(a+x)/(a-x)| + C
**By partial fractions:** 1/(a² - x²) = 1/((a-x)(a+x)) = (1/2a)(1/(a-x) + 1/(a+x)).
**Integrating:** (1/2a) ln |(a+x)/(a-x)| + C. Note difference from ∫ dx/(a² + x²) = (1/a) arctan(x/a) + C.
Keep practising Unit 6A: Indefinite Integrals & Fundamental Theorem
Browse all Unit 6A: Indefinite Integrals & Fundamental Theorem questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
The integrating factor of the linear differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} The number of arbitrary constants in the general solution of a differential equation of orUsing the substitution $t = 1 + x^2$, $\displaystyle\int \dfrac{x}{1 + x^2}\,dx$ equals:$\displaystyle\int e^x\bigl(f(x) + f'(x)\bigr)\,dx$ equals:$\displaystyle\int \log x\,dx$ equals:$\displaystyle\int ec^2 x\,dx$ equals:$\displaystyle\int \dfrac{1}{ qrt{1 - x^2}}\,dx$ equals:$\displaystyle\int \dfrac{1}{1+x^2}\,dx$ equals: