Standard Integrals Reference Table

Integral	Result
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 $\frac{dx}{a^2-x^2}$	$\frac{1}{2a}$ ln\| $\frac{a+x}{(a-x)}$ \| + 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
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
integral e^(ax)sin(bx) dx	e^(ax)(asin(bx)-bcos(bx))/( $a^{2+b}^2$ ) + C
integral e^(ax)cos(bx) dx	e^(ax)(acos(bx)+bsin(bx))/( $a^{2+b}^2$ ) + C