CBSE Class 12 Mathematics — Integrals

If $\int \frac{3ax}{b^2 + c^2 x^2}\,dx = A \log |b^2 + c^2 x^2| + K$, then the value of A is

The value of $\int_{-1}^{1} \frac{x^3}{x^2+2|x|+1}\,dx$ is

Evaluate: integral from 0 to 1 of $x \tan^{-1} x \, dx$.

(a) Find: $\int \sqrt{\dfrac{x+2}{x-2}} \, dx$. OR (b) Find: $\int \dfrac{x^2}{(x^2+9)(x^2+16)} \, dx$.

If I_1 = integral from -pi/4 to pi/4 of dx/(1 + cos 2x) and I_2 = integral from -1/2 to 1/2 of |x| dx, then show that $I_1 - 4 I_2 = 0$.