Standard Integrals

A collection of vocabulary flashcards covering basic and trigonometric standard integrals based on the lecture notes.

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

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

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

$$\sin(x) + C$$

$$\int \sec^2(x)\,dx$$

$$\tan(x) + C$$

$$\int \text{cosec}^2(x)\,dx$$

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

$$\int \sec(x)\tan(x)\,dx$$

$$\sec(x) + C$$

$$\int \text{cosec}(x)\cot(x)\,dx$$

$$-\text{cosec}(x) + C$$

$$\int \frac{1}{x}\,dx$$

$$\ln(x) + C$$

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

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

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

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

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

$$e^x + C$$

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

$$\ln(\sec(x)) + C$$

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

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

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

$$\ln|\sec(x) + \tan(x)| + C$$

$$\int \text{cosec}(x)\,dx$$

$$\ln|\text{cosec}(x) - \cot(x)| + C$$

$$\int \frac{1}{\sqrt{1-x^2}}\,dx$$

$$\sin^{-1}(x) + C$$

$$\int \frac{1}{1+x^2}\,dx$$

$$\tan^{-1}(x) + C$$