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

Standard Integrals:

• integral $\frac{dx}{x^2+a^2}$ = $\frac{1}{a}$arctan$\frac{x}{a}$ + C
• integral $\frac{dx}{x^2-a^2}$ = $\frac{1}{2a}$ln|$\frac{x-a}{(x+a)}$| + C
• integral dx/sqrt(a^{2-x}^2) = arcsin$\frac{x}{a}$ + 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 = $\frac{x}{2}$sqrt(a^{2-x}^2) + ($a^2$/2)arcsin$\frac{x}{a}$ + C
• integral sqrt(x^{2+a}^2) dx = $\frac{x}{2}$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_$\frac{n-2}{n}$
• $cos^n$: $J_n$ = cos^(n-1)x sinx/n + (n-1)J_$\frac{n-2}{n}$
• $tan^n$: $K_n$ = tan^(n-1)$\frac{x}{n-1}$ - K_(n-2)
• $sec^n$: $L_n$ = sec^(n-2)x $\frac{tanx}{n-1}$ + (n-2)L_$\frac{n-2}{(n-1)}$
• $x^n$$e^x$: $M_n$ = $x^n$$e^x$ - n*M_(n-1)

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

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

Weierstrass: t = tan$\frac{x}{2}$: sinx = 2$\frac{t}{1+t^2}$, cosx = $\frac{1-t^2}{(1+t^2)}$, dx = 2$\frac{dt}{1+t^2}$

Exponential-Trig: integral e^(ax)sin(bx)dx = e^(ax)$\frac{a*sinbx - b*cosbx}{(a^2+b^2)}$ + C