Tabella integrali notevoli

$$\int f'(x)dx=f(x)+c$$

$$\int adx=ax+c$$

$$\int x^ndx=\frac{x^{n+1}}{n+1}+c,\quad con\quad n\neq -1$$

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

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

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

$$\int \frac{1}{cos^2x}dx=\int (1+tan^2x)dx=tanx+c$$

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

$$\int e^xdx=e^x+c$$

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

$$\int \frac{1}{1+x^2}dx=arctan(x)+c$$

$$\int \frac{1}{\sqrt{1-x^2}}dx=arcsin(x)+c$$

$$\int -\frac{1}{\sqrt{1-x^2}}dx=arccos(x)+c$$

$$\int sinh(x)dx=cosh(x)+c$$

$$\int cosh(x)dx=sinh(x)+c$$