integral

$$\int dx$$

$$x + C$$

$$\int x^n\,dx$$

$$\frac{x^{n+1}}{n+1} + C$$

$$\int x^a\,dx$$

$$\frac{x^{a+1}}{a+1} + C$$

$$\int \frac{dx}{x}$$

$$\ln|x| + C$$

$$\int a^x\,dx$$

$$\frac{a^x}{\ln(a)} + C$$

$$\int e^x\,dx$$

$$e^x + C$$

$$\int \sin(x)\,dx$$

$$-\cos(x) + C$$

$$\int \cos(x)\,dx$$

$$\sin(x) + C$$

$$\int \frac{dx}{\cos^2(x)}$$

$$\operatorname{tg}(x) + C$$

$$\int \frac{dx}{\sin^2(x)}$$

$$-\operatorname{ctg}(x) + C$$

$$\int \operatorname{tg}(x)\,dx$$

$$-\ln|\cos(x)| + C$$

$$\int \operatorname{ctg}(x)\,dx$$

$$\ln|\sin(x)| + C$$

$$\int \frac{dx}{x^2 - a^2}$$

$$\frac{1}{2a}\ln\left|\frac{x - a}{x + a}\right| + C$$

$$\int \frac{dx}{x^2 + a^2}$$

$$\frac{1}{a}\operatorname{arctg}\left(\frac{x}{a}\right) + C$$

$$\int \frac{dx}{\sqrt{a^2 - x^2}}$$

$$\arcsin\left(\frac{x}{a}\right) + C$$

$$\int \frac{dx}{\sqrt{x^2 + a^2}}$$

$$\ln\left(x + \sqrt{x^2 + a^2}\right) + C$$

$$\int \frac{dx}{\sqrt{x^2 - a^2}}$$

$$\ln\left|x + \sqrt{x^2 - a^2}\right| + C$$

$$\int \sqrt{x^2 - a^2}\,dx$$

$$\frac{1}{2}\left(x\sqrt{x^2 - a^2} - a^2\ln\left|x + \sqrt{x^2 - a^2}\right|\right) + C$$

$$\int \sqrt{x^2 + a^2}\,dx$$

$$\frac{1}{2}\left(x\sqrt{x^2 + a^2} + a^2\ln\left|x + \sqrt{x^2 + a^2}\right|\right) + C$$

$$\int \sqrt{a^2 - x^2}\,dx$$

$$\frac{1}{2}\left(x\sqrt{a^2 - x^2} + a^2\arcsin\left(\frac{x}{a}\right)\right) + C$$