$$\int 0 dx = C \tag1$$

$$\int x^a dx = \frac{1}{a + 1} x^{a + 1} + C \quad (a \ne -1 ) \tag2$$

$$\int \frac{1}{x} dx = \ln|x| + C \tag3$$

$$\int a^x dx = \frac{a^x}{\ln a} + C \quad (a > 0, a \ne 1) \tag4$$

$$\int e^x dx = e^x + C \tag5$$

$$\int sinx dx = -cosx + C \tag6$$

$$\int cosx dx = sinx + C \tag7$$

$$\int sec^2x dx = tanx + C \tag8$$

$$\int csc^2x dx = -cotx + C \tag9$$

$$\int secx \, tanx \, dx = secx + C \tag{10}$$

$$\int cscx \, cotx \, dx = -cscx + C \tag{11}$$

$$\int \frac{1}{\sqrt{1 – x^2}} dx = arcsinx + C \tag{12}$$

$$\int \frac{1}{1 + x^2} dx = arctanx + C \tag{13}$$

$$\int \frac{dx}{\sqrt{a^2 – x^2}} = arcsin\frac{x}{a} + C \tag{14}$$

$$\int \frac{dx}{a^2 + x^2} = \frac{1}{a} arctan\frac{x}{a} + C \tag{15}$$

$$\int \frac{dx}{x^2 – a^2} = \frac{1}{2a} \left| \ln \frac{x – a}{x + a} \right| + C \tag{16}$$

$$\int \frac{dx}{\sqrt{x^2 + a^2}} = \ln (x + \sqrt{x^2 + a^2}) + C \tag{17}$$

$$\int \frac{dx}{\sqrt{x^2 – a^2}} = \ln \left| x + \sqrt{x^2 – a^2} \right| + C \tag{18}$$

$$\int secx dx = \ln \left| secx + tanx \right| + C \tag{19}$$

$$\int cscx dx = – \ln \left| cscx + cotx \right| + C \tag{20}$$