Basic Integration Formulas

• \( \int 0 \, dx = C \)
• \( \int 1 \, dx = x + C \)
• \( \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \), where \( n \neq -1 \)
• \( \int \frac{1}{x} \, dx = \ln|x| + C \)

Trigonometric Functions

• \( \int \sin x \, dx = -\cos x + C \)
• \( \int \cos x \, dx = \sin x + C \)
• \( \int \sec^2 x \, dx = \tan x + C \)
• \( \int \csc^2 x \, dx = -\cot x + C \)
• \( \int \sec x \tan x \, dx = \sec x + C \)
• \( \int \csc x \cot x \, dx = -\csc x + C \)

Inverse Trigonometric Functions

• \( \int \frac{1}{\sqrt{1-x^2}} \, dx = \sin^{-1} x + C \)
• \( \int \frac{-1}{\sqrt{1-x^2}} \, dx = \cos^{-1} x + C \)
• \( \int \frac{1}{1+x^2} \, dx = \tan^{-1} x + C \)

Exponential Functions

• \( \int e^x \, dx = e^x + C \)
• \( \int a^x \, dx = \frac{a^x}{\ln a} + C \), where \( a > 0 \) and \( a \neq 1 \)

Logarithmic Functions

• \( \int \ln x \, dx = x \ln x – x + C \)
• \( \int \log_a x \, dx = \frac{x \log_a x – x}{\ln a} + C \), where \( a > 0 \) and \( a \neq 1 \)