Anti Derivatives

∫ k dx

kx + c

∫ x^n dx

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

∫ sinx dx

-cosx + c

∫ cosx dx

sinx + c

∫ sec^2x dx

tanx + c

∫ e^x dx

e^x + c

∫ 1/x dx

ln lxl + c

∫ a^x dx

(a^x/ lna) + c

Finds the area under the curve

definite integral

purely algebraic antiderivative of a function

indefinite integral

The integral from a to b is equal to the antiderivative at a minus the antiderivative at b.

FTC

The unknown value that must be added to the antiderivative.

C

∫ 1/(1+x^2) dx

Arctanx + c

∫ secx tanx dx

Secx + C

∫ -cotx cscx dx

Csc+ C

∫ -csc^2 x dx

Cot x+ C

∫ 1/ ( 1-x^2 )^(1/2) dx

ArcSin+ C

∫ 1/ ( 1+x^2 )^(1/2) dx

ArcCosx+C