Integrals of special forms
Indefinite integration · Mathematics
Study notes
Q: Evaluate the integral of dx/(4+x^2). Pattern: integral of dx/(a^2+x^2) = (1/a) tan^(-1)(x/a) + C, with a^2 = 4 so a = 2. Answer: (1/2) tan^(-1)(x/2) + C. Check: differentiate (1/2) tan^(-1)(x/2): (1/2)(1/(1+x^2/4))(1/2) = 1/(4+x^2). Correct!