Common Integrals

\int dx=

x+C

∫kdx=

kx+C

∫\frac{1}{x}dx=

ln|x|+C

∫x^{-1}dx=

ln|x|+C

\int\frac{1}{ax+b}dx=

\frac{1}{a}ln|ax+b|+C

∫cos(x)dx=

sin(x)+C

∫sin(x)dx=

-cos(x)+C

∫sec^2(x)dx=

tan(x)+C

∫sec(x)tan(x)dx=

sec(x)+C

∫csc(x)cot(x)dx=

-csc(x)+C

∫csc^2(x)dx=

-cot(x)+C

∫tan(x)dx=

-ln|cos(x)|+C=ln|sec(x)|+C

∫cot(x)dx=

ln|sin(x)|+C=-ln|csc(x)|+C

∫sec(x)dx=

ln|sec(x)+tan(x)|+C

∫sec^3(x)dx=

\frac12[sec(x)tan(x)+ln|sec(x)+tan(x)|]+C

∫csc(x)dx=

ln|csc(x)-cot(x)|+C

∫csc^3(x)dx=

\frac12[-csc(x)cot(x)+ln|csc(x)-cot(x)|]+C

\int\frac{1}{\sqrt{a^2+x^2}}dx=

sin^{-1}(\frac{x}{a})+C

∫sin^{-1}(x)dx=

xsin^{-1}(x)+\sqrt{1-x^2}+C

\int\frac{1}{a^2+x^2}dx=

\frac{1}{a}tan^{-1}(\frac{x}{a})+C

∫tan^{-1}(x)dx=

xtan^{-1}(x)-\frac12ln(1+x^2)+C

\int\frac{1}{x\sqrt{x^2-a^2}}dx=

(\frac{1}{a})sec^{-1}(\frac{x}{a})+C

∫cos^{-1}(x)dx=

xcos^{-1}(x)-\sqrt{1-x^2}+C