Standard Integrals Reference Table

Integral	Result
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/(a^2-x^2)	(1/2a)ln\|(a+x)/(a-x)\| + 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
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
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