∫ dx = ∫ 1 dx = x + c, for x∈R.

∫ x^{a} dx = \frac{x^{a+1}}{a + 1} + c, for a∈R, a ≠ −1, x∈R − \{0\}.

∫ \frac{dx}{x} = ln |x| + c, for x∈R − \{0\}.

∫ \frac{f′(x)}{f(x)} dx = ln |f(x)| + c, for f(x)≠0, x∈D(f).

∫ e^{ax} dx = \frac{e^{ax}}{a} + c,  for a∈R, a ≠ 0, x∈R,  ∫ e^{x} dx = e^{x} + c.
∫ a^{x} dx = \frac{a^{x}}{ln a} + c,  for a > 0, a ≠ 1, x∈R,  ∫ e^{x} dx = \begin{matrix}e & x \\ ln & e \end{matrix} + c = e^{x} + c.
∫ sin ax dx = −\frac{cos ax}{a} + c,  for a∈R, a ≠ 0, x∈R,  ∫ sin x dx = − cos x + c.
∫ cos ax dx = \frac{sin ax}{a} + c,  for a∈R, a ≠ 0, x∈R,  ∫ cos x dx = sin x + c.

∫ \frac{dx}{cos^{2} ax} = \frac{tg ax}{a} + c, for a∈R, a ≠ 0, x∈R − \{(2k + 1)\frac{π}{2} ; k ∈Z\}, ∫ \frac{dx}{cos^{2} x} = tg x + c.

∫ \frac{dx}{sin^{2} ax} = −\frac{cotg ax}{a} + c, for a∈R, a ≠ 0, x∈R − \{kπ; k ∈Z\}, ∫ \frac{dx}{sin^{2} x} = − cotg x + c.

∫ \frac{dx}{\sqrt{a^{2} − x^{2}}} = arcsin \frac{x}{|a|} + c_{1} = − arccos \frac{x}{|a|} + c_{2}, for a∈R, a ≠ 0, x∈(− |a|; |a|).

∫ \frac{dx}{\sqrt{x^{2} − a^{2}}} = ln |x + \sqrt{x^{2} − a^{2}}| + c, for a∈R, a ≠ 0, x∈(−∞; − |a|) ∪ (|a|; ∞).

∫ \frac{dx}{\sqrt{x^{2} + a^{2}}} = ln (x + \sqrt{x^{2} + a^{2}}) + c, for a∈R, a ≠ 0, x∈R.

∫ \frac{dx}{x^{2} + a^{2}} = \frac{1}{a} arctg \frac{x}{a} + c_{1} = −\frac{1}{a} arccotg \frac{x}{a} + c_{2}, for a∈R, a ≠ 0, x∈R.

∫ \frac{dx}{x^{2} − a^{2}} = ∫ \frac{1}{2a} [\frac{1}{x − a} − \frac{1}{x + a}] dx = \frac{1}{2a} ln |\frac{x − a}{x + a}| + c, for a∈R, a ≠ 0, x∈R − \{±a\}.

∫ sinh ax dx = \frac{cosh ax}{a} + c,  for a∈R, a ≠ 0, x∈R,  ∫ sinh x dx = cosh x + c.
∫ cosh ax dx = \frac{sinh ax}{a} + c,  for a∈R, a ≠ 0, x∈R,  ∫ cosh x dx = sinh x + c.
∫ \frac{dx}{cosh^{2} ax} = \frac{tgh ax}{a} + c,  for a∈R, a ≠ 0, x∈R,  ∫ \frac{dx}{cosh^{2} x} = tgh x + c.
∫ \frac{dx}{sinh^{2} ax} = −\frac{cotgh ax}{a} + c,  for a∈R, a ≠ 0, x∈R − \{0\},  ∫ \frac{dx}{sinh^{2} x} = − cotgh x + c.