Интегрирование функций

∫kf(x)dx = k ∫f(x)dx

∫(u ± v)dx = ∫udx ± ∫vdx

∫udv = uv − ∫vdu

∫ 0dx = C

∫ xⁿdx = $\frac{x^{n + 1}}{n + 1}$ + C

∫(ax + b)ⁿdx = $\frac{{(a x + b)}^{n + 1}}{a (n + 1)}$ + C

∫ $\frac{d x}{x}$ = ln|x| + C

∫ $\frac{d x}{a x + b} = \frac{1}{a}$ ln|ax + b| + C

∫ a^xdx = $\frac{a^{x}}{ln a}$ + C

∫ e^xdx = e^x + C

∫ sin x dx = −cos x + C

∫ cos x dx = sin x + C

∫ tg x dx = −ln|cos x| + C

∫ ctg x dx = ln|sin x| + C

∫ $\frac{d x}{{sin}^{2} x}$ = −ctg x + C

∫ $\frac{d x}{{cos}^{2} x}$ = tg x + C

∫ $\frac{d x}{\sqrt{a^{2} - x^{2}}} = arcsin \frac{x}{a}$ + C

∫ $\frac{d x}{a^{2} + x^{2}} = \frac{1}{a} arctg \frac{x}{a}$ + C

∫ $\frac{d x}{a^{2} - x^{2}} = \frac{1}{2 a} ln | \frac{a + x}{a - x} |$ + C

∫ $\frac{d x}{\sqrt{a^{2} \pm x^{2}}} = ln | x + \sqrt{x^{2} \pm a^{2}} |$ + C

∫ $\frac{a x + b}{c x + d} d x = \frac{a}{c} x + \frac{b c - a d}{c^{2}}$ ln|cx + d| + C