# Integration Formulas or Antiderivatives

In calculus, an indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f.

## Integration Rules

Function Integral
$$\int 0dx$$ $$C$$
$$\int 1dx$$ $$x+C$$
$$\int adx$$ $$ax+C$$
$$\int xdx$$ $$\frac{x^{2}}{2}+C$$
$$\int x^{2}dx$$ $$\frac{x^{3}}{3}+C$$
$$\int x^{n}dx$$ $$\frac{x^{n+1}}{n+1}+C$$
$$\int \frac{1}{x}dx$$ $$\ln\left | x \right |+C$$
$$\int \frac{1}{\sqrt{x}}dx$$ $$2\sqrt{x}+C$$
$$\int a^{x}dx, \textrm {kus}\;$$ $$a>0\;\textrm {and}\;a\neq 1$$ $$\frac{a^{x}}{\ln a}+C$$
$$\int \sin xdx$$ $$-\cos x+C$$
$$\int \cos xdx$$ $$\sin x+C$$
$$\int \tan xdx$$ $$-\ln\left | \cos x \right |+C$$
$$\int \cot xdx$$ $$\ln\left | \sin x \right |+C$$
$$\int \frac{1}{\cos^{2} x}dx$$ $$\tan x+C$$
$$\int \frac{1}{\sin^{2} x}dx$$ $$-\cot x+C$$
$$\int \frac{1}{\sqrt{1-x^{2}}}dx$$ $$\arcsin x + C$$
$$\int -\frac{1}{\sqrt{1-x^{2}}}dx$$ $$\arccos x + C$$
$$\int \frac{1}{1+x^{2}}dx$$ $$\arctan x + C$$
$$\int -\frac{1}{1+x^{2}}dx$$ $$\textrm{arccot}\,x + C$$