formulario integrali immediati

$\int f(x)dx=F(x)+c\iff F^{\prime }(x)=f(x)$

${\int }_a^{b}f(x)dx=F(b)-F(a)$

$\int k\cdot f(x)dx=k\cdot \int f(x)dx$

$\int [f(x)\pm g(x)]dx=\int f(x)dx\pm \int g(x)dx$

$\int f^{\prime }(x)dx=f(x)+c$

$\int ndx=nx+c$

$\int \frac{1}{x}dx=\ln (|x|)+c$

$\int x^{n}dx=\frac{x^{n+1}}{n+1}+c$

$\int e^{x}dx=e^x+c$

$\int e^{kx}dx=\frac{e^{kx}}{k}+c$

$\int a^{x}dx=\frac{a^x}{ln(a)}+c$

$\int sin(x)dx=-cos(x)+c$

$\int cos(x)dx=sin(x)+c$

$\int (1+t{g}^2(x))dx=\int \frac{1}{co{s}^2(x)}dx=tg(x)+c$

$\int (1+{\cot }^2(x))dx=\int \frac{1}{si{n}^2(x)}dx=-\cot (x)+c$

$\int \frac{1}{sin(x)}dx=ln(|\frac{tg(x)}{2}|)+c$

$\int \frac{1}{cos(x)}dx=ln(|\frac{tg(x)}{2}+\frac{\pi }{4}|)+c$

$\int si{n}^2(x)dx=\frac{1}{2}(x-sin(x)cos(x))+c$

$\int co{s}^2(x)dx=\frac{1}{2}(x+sin(x)cos(x))+c$