Partial Fractions: P/Q = polynomial + sum of A/(x-a)^k + (Bx+C)/(x^2+px+q)^k

Standard Integrals:

• integral dx/(x^2+a^2) = (1/a)arctan(x/a) + C
• integral dx/(x^2-a^2) = (1/2a)ln|(x-a)/(x+a)| + C
• integral dx/sqrt(a^2-x^2) = arcsin(x/a) + C
• integral dx/sqrt(x^2+a^2) = ln|x+sqrt(x^2+a^2)| + C
• integral dx/sqrt(x^2-a^2) = ln|x+sqrt(x^2-a^2)| + C
• integral sqrt(a^2-x^2) dx = (x/2)sqrt(a^2-x^2) + (a^2/2)arcsin(x/a) + C
• integral sqrt(x^2+a^2) dx = (x/2)sqrt(x^2+a^2) + (a^2/2)ln|x+sqrt(x^2+a^2)| + C

Reduction Formulas:

• sin^n: I_n = -sin^(n-1)x cosx/n + (n-1)I_(n-2)/n
• cos^n: J_n = cos^(n-1)x sinx/n + (n-1)J_(n-2)/n
• tan^n: K_n = tan^(n-1)x/(n-1) - K_(n-2)
• sec^n: L_n = sec^(n-2)x tanx/(n-1) + (n-2)L_(n-2)/(n-1)
• x^ne^x: M_n = x^ne^x - n*M_(n-1)

Wallis: W_n = (n-1)/n * (n-3)/(n-2) * ... * {pi/2 if n even, 1 if n odd}

Special: integral e^x[f+f'] dx = e^x*f(x) + C

Weierstrass: t = tan(x/2): sinx = 2t/(1+t^2), cosx = (1-t^2)/(1+t^2), dx = 2dt/(1+t^2)

Exponential-Trig: integral e^(ax)sin(bx)dx = e^(ax)(asinbx - bcosbx)/(a^2+b^2) + C