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Commonly Used Integrals


\(\int dx = x + c\)

\(\int k\:dx = kx+c\)

\(\int x^n\: dx = {1 \over{n+1}}x^{n+1}+c\)

\(\int {1 \over x}\: dx = ln|x| + c\)

\(\int {x^{-n}}\: dx = {1 \over{-n+1}}x^{-n+1}+c\)

\(\int {1 \over {ax+b}}\: dx = {1 \over a}ln |ax+b| + c\)

\(\int {sin(u)}\: du = -cos(u)+c\)

\(\int {cos(u)}\: du = sin(u)+c\)

\(\int {tan(u)}\: du = ln|cos(u)|+c\)

\(\int {e^u}\: du = e^u+c\)

\(\int {a^u}\: du = {a^u \over ln(a)}+c\)

\(\int {ln(u)}\: du = u\:ln(u)-u+c\)

\(\int {sin^{-1}(u)}\: du = u\:sin^{-1}(u)+\sqrt{1-u^2}+c\)

\(\int {cos^{-1}(u)}\: du = u\:cos^{-1}(u)+\sqrt{1-u^2}+c\)

\(\int {tan^{-1}(u)}\: du = u\:tan^{-1}(u)+{1 \over 2}ln(1+u^2)+c\)



A List of Integrals



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