1What is the result of $\int k \, dx$?
$ kx + C, \quad k \text{ any number} $
2What is the result of $\int x^n \, dx$?
$ \frac{x^{n+1}}{n+1} + C, \quad n \neq -1 $
3What is the result of $\int \frac{dx}{x}$?
$ \ln |x| + C $
4What is the result of $\int e^x \, dx$?
$ e^x + C $
5What is the result of $\int a^x \, dx$?
$ \frac{a^x}{\ln a} + C, \quad (a > 0, a \neq 1) $
6What is the result of $\int \sin x \, dx$?
$ -\cos x + C $
7What is the result of $\int \cos x \, dx$?
$ \sin x + C $
8What is the result of $\int \sec^2 x \, dx$?
$ \tan x + C $
9What is the result of $\int \csc^2 x \, dx$?
$ -\cot x + C $
10What is the result of $\int \sec x \tan x \, dx$?
$ \sec x + C $
11What is the result of $\int \csc x \cot x \, dx$?
$ -\csc x + C $
12What is the result of $\int \tan x \, dx$?
$ \ln |\sec x| + C $
13What is the result of $\int \cot x \, dx$?
$ \ln |\sin x| + C $
14What is the result of $\int \sinh x \, dx$?
$ \cosh x + C $
15What is the result of $\int \cosh x \, dx$?
$ \sinh x + C $
16What is the result of $\int \frac{dx}{\sqrt{a^2 - x^2}}$?
$ \arcsin \frac{x}{a} + C $
17What is the result of $\int \frac{dx}{a^2 + x^2}$?
$ \frac{1}{a} \arctan \frac{x}{a} + C $
18What is the result of $\int \frac{dx}{x\sqrt{x^2 - a^2}}$?
$ \frac{1}{a} \arcsec \left| \frac{x}{a} \right| + C $
19What is the result of $\int \frac{dx}{\sqrt{a^2 + x^2}}$?
$ \sinh^{-1} \frac{x}{a} + C, \quad (a > 0) $
20What is the result of $\int \frac{dx}{\sqrt{x^2 - a^2}}$?
$ \cosh^{-1} \frac{x}{a} + C, \quad (x > a > 0) $