Properties of Integrals

Integration rules

∫cf(x) dx=

c∫f(x) dx

∫\[f(x)+g(x) dx=

∫f(x) dx+ ∫g(x) dx

∫k dx=

kx+C

∫x^n dx=

(x^(n+1))/(n+1))+C

∫1/x dx=

ln(x)+C

∫e^x dx=

e^x+C

∫a^x dx=

(a^x)/(ln(a))+C

∫sin(x) dx

\-cos(x)+C

∫cos(x) dx

sin(x)+C

∫sec^2(x) dx=

tan(x)+C

∫csc^2(x) dx=

\-cot(x)+C

∫sec(x)tan(x) dx=

sec(x)+C

∫csc(x)cot(x) dx=

\-csc(x)+C

∫1/(√(1+x^2)) dx=

tan^-1(x)+C

∫1/(√(1-x^2)) dx=

sin^-1(x)+C

∫1/(x√(x^2-1)) dx=

sec^-1(x)+C