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Taulukko alkeisfunktioiden integraalifunktioista

(1) $$\begin{split}\begin{array}{ccl}\hline && \\[-3ex] f(x) & \int f(x)\,\d x & \text{Määrittelyjoukko} \\[1ex]\hline &&\\[-1ex] x^n & \dfrac{x^{n + 1}}{n + 1} + C & n \in \Z \setminus \{-1\}, \text{ ei määritelty pisteessä } 0 \text{ jos } n < 0 \\[3ex] x^a & \dfrac{x^{a + 1}}{a + 1} + C & a \in \R \setminus \{-1\}, \text{ määritelty kun } x > 0 \\[3ex] \dfrac{1}{x} & \ln|x| + C & \text{ei määritelty pisteessä } 0 \\[3ex] e^x & e^x + C & \text{määrittelyjoukko koko } \mathbb{R}\\[3ex] \sin x & -\cos x + C & \text{määrittelyjoukko koko } \mathbb{R}\\[3ex] \cos x & \sin x + C & \text{määrittelyjoukko koko } \mathbb{R}\\[3ex] \tan x & -\ln\left|\cos x\right| + C & \text{ei määritelty pisteissä } \dfrac{\pi}{2} + n\pi,\ n \in \Z \\[3ex] \dfrac{1}{\tan x} & \ln\left|\sin x\right| + C & \text{ei määritelty pisteissä } n\pi,\ n \in \Z \\[3ex] \dfrac{1}{\cos^2 x} & \tan x + C & \text{ei määritelty pisteissä } \dfrac{\pi}{2} + n\pi,\ n \in \Z \\[3ex] \dfrac{1}{\sin^2 x} & -\dfrac{1}{\tan x} + C & \text{ei määritelty pisteissä } n\pi,\ n \in \Z \\[3ex] \dfrac{1}{\sqrt{1 - x^2}} & \arcsin x + C & \text{määritelty kun } {-1} < x < 1 \\[3ex] \dfrac{1}{1 + x^2} & \arctan x + C & \text{määrittelyjoukko koko } \mathbb{R} \\[3ex] \dfrac{1}{\sqrt{1 + x^2}} & \arsinh x + C & \text{määrittelyjoukko koko } \mathbb{R} \\[3ex] \dfrac{1}{\sqrt{x^2 - 1}} & \arcosh x + C & \text{ei määritelty kun } {-1} < x < 1 \\[3ex] \dfrac{1}{1 - x^2} & \artanh x + C & \text{määritelty kun } {-1} < x < 1 \\[3ex]\hline \end{array}\end{split}$$

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