Tabla de Primitivas

función f(x) intervalo I

primitivas de f(x)

x^{n} (n ∈ ℕ)  I = ℝ  \frac{x^{n+1}}{n+1} + k

x^{α} (α ∈ ℝ, α ≠ −1)  I = ℝ^{+}  \frac{x^{α+1}}{α+1} + k

\frac{1}{x}  I = ℝ^{+}  L(x) + k

\frac{1}{x}  I = ℝ^{−}  L|x| + k

e^{ax}  I = ℝ  \frac{e^{ax}}{a} + k

a^{x} (a ∈ ℝ^{+}, a ≠ 1)  I = ℝ  \frac{a^{x}}{L(a)} + k

sen(ax)  I = ℝ  \frac{−cos(ax)}{a} + k

cos(ax)  I = ℝ  \frac{sen(ax)}{a} + k

\frac{1}{a^{2}+x^{2}}  I = ℝ  \frac{1}{a} Arctg (\frac{x}{a}) + k

1 + tg^{2}(x) = \frac{1}{cos^{2}(x)}  I = (−\frac{π}{2}, \frac{π}{2})  tg(x) + k

\frac{1}{\sqrt{a^{2}−x^{2}}}  I = (−a, a)  Arcsen (\frac{x}{a}) + k

\frac{1}{\sqrt{a^{2}+x^{2}}}  I = ℝ  {L (x + \sqrt{a^{2} + x^{2}}) + \atop k}

sh(ax)  I = ℝ  \frac{ch(ax)}{a} + k

ch(ax)  I = ℝ  \frac{sh(ax)}{a} + k