Integral List

Basic

Rule Name Integral
\( \int dx = x + C \)
\( \int x^n dx = \dfrac {x^{n+1}}{n+1} + C \)
\( \int \dfrac 1x dx = \ln{|x|} + C \)
\( \int a^x dx = \dfrac {a^x}{lna} + C \)
\( \int e^x dx = e^x + C \)

Trig

Rule Name Integral
\( \int cos(x) dx = sin(x) + C \)
\( \int sin(x) dx = -cos(x) + C \)
\( \int cot(x) dx = ln{|sin(x)|} + C \)
\( \int csc(x) dx = -ln{|csc(x) + cot(x)|} + C \)
\( \int csc^2(x) dx = -cot(x) + C \)
\( \int csc(x)cot(x) dx = -csc(x) + C \)
\( \int tan(x) dx = -ln{|cos(x)|} + C \)
\( \int sec(x) dx = ln{|sec(x) + tan(x)|} + C \)
\( \int sec^2(x) dx = tan(x) + C \)
\( \int sec(x)tan(x) dx = sec(x) + C \)

Inverse Trig

Rule Name Integral
\( \int \dfrac{1}{\sqrt{a^2-x^2}} dx = arcsin\dfrac xa + C \)
\( \int \dfrac 1{a^2 + x^2} dx = \dfrac {1}{a}arctan\dfrac xa + C \)
\( \int \dfrac 1{x\sqrt{x^2 - a^2}} dx = \dfrac {1}{a}arcsec\dfrac {|x|}a + C \)