Must-Know Results:

• integral$\frac{0 to pi}{2}$ $sin^n$ $\frac{x}{sin^n x + cos^n x}$ dx = pi/4
• integral$\frac{0 to pi}{2}$ ln(sin x) dx = integral$\frac{0 to pi}{2}$ ln(cos x) dx = -$\frac{pi}{2}$*ln 2
• integral(0 to pi) x*f(sin x) dx = $\frac{pi}{2}$*integral(0 to pi) f(sin x) dx
• integral(0 to 1) x^(m-1)(1-x)^(n-1) dx = (m-1)!(n-1)!/(m+n-1)! for positive integers
• integral(0 to infinity) e^(-$x^2$) dx = sqrt$\frac{pi}{2}$ (Gaussian integral)
• integral$\frac{0 to pi}{2}$ sin x dx = integral$\frac{0 to pi}{2}$ cos x dx = 1
• integral(0 to 1) $\frac{1}{1+x^2}$ dx = pi/4