Integral Rules

∫xⁿ dx

(xⁿ⁺¹)/n+1+C

∫k dx

kx+C

∫0 dx

C

∫1/x dx

ln|x|

∫e^x dx

e^x+C

∫e^kx dx

(e^kx/k)+C

∫cos(x) dx

sin(x)+C

∫sin(x) dx

-cos(x)+C

∫cos(kx) dx

sin(kx)/k +C

∫sin(kx) dx

-cos(kx)/k -cos(kx)+C

∫sec²(x) dx

tan(x)+C

∫sec²(kx) dx

tan(kx)/k+C

∫tan(x)sec(x) dx

sec(x)+C

∫tan(kx)sec(kx) dx

sec(kx)/k+C

∫cot(x)csc(x) dx

-csc(x)+C

∫cot(kx)csc(kx) dx

-csc(kx)/k+C

∫csc²(x) dx

-cot(x)+C

∫csc²(kx) dx

-cot(kx)/k+C

∫1/(√1-x²) dx

sin^-1(x)+C or -cos^-1(x)+C

∫1/(√k²-x²) dx

sin^-1(x/h) or -cos^-1(x/h)+C

-1/(√1-x²) dx

cos^-1(x)+C

1/(1+x²) dx

tan^-1(x)+C

1/(k²+x²) dx

tan^-1(x)/k+C