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\(\int dx = x + c\) \(\int k\:dx = kx+c\) \(\int x^n\: dx = {1 \over{n+1}}x^{n+1}+c\) \(\int {1 \over x}\: dx = ln|x| + c\) \(\int {x^{-n}}\: dx = {1 \over{-n+1}}x^{-n+1}+c\) \(\int {1 \over {ax+b}}\: dx = {1 \over a}ln |ax+b| + c\) \(\int {sin(u)}\: du = -cos(u)+c\) \(\int {cos(u)}\: du = sin(u)+c\) |
\(\int {tan(u)}\: du = ln|cos(u)|+c\) \(\int {e^u}\: du = e^u+c\) \(\int {a^u}\: du = {a^u \over ln(a)}+c\) \(\int {ln(u)}\: du = u\:ln(u)-u+c\) \(\int {sin^{-1}(u)}\: du = u\:sin^{-1}(u)+\sqrt{1-u^2}+c\) \(\int {cos^{-1}(u)}\: du = u\:cos^{-1}(u)+\sqrt{1-u^2}+c\) \(\int {tan^{-1}(u)}\: du = u\:tan^{-1}(u)+{1 \over 2}ln(1+u^2)+c\) |