Leibniz integral rule: d/da integral(alpha(a) to beta(a)) f(x,a) dx = integral(alpha to beta) $\frac{df}{da}$ dx + f(beta,a)*beta'(a) - f(alpha,a)*alpha'(a)

Feynman's technique: Introduce a parameter, differentiate with respect to it, evaluate the simpler integral, then integrate back.

Example: Compute integral(0 to 1) $\frac{x^a - 1}{ln}$(x) dx. Let I(a) = integral(0 to 1) $\frac{x^a - 1}{ln}$(x) dx. Then I(0) = 0. I'(a) = integral(0 to 1) $x^a$ dx = $\frac{1}{a+1}$. I(a) = ln(a+1) + C. I(0) = 0 gives C = 0. So I(a) = ln(a+1).

JEE relevance: Occasionally tested in JEE Advanced. The technique is powerful but rarely needed for JEE Main.