Integral Formulas

Integral Formulas

• General Integral Formulas:

  • ( \int u^n , du = \frac{1}{n+1}u^{n+1} + C )

  • ( \int \sin(u) , du = -\cos(u) + C )

  • ( \int \cos(u) , du = \sin(u) + C )

  • ( \int e^u , du = e^u + C )

  • ( \int \ln(u) , du = u \ln(u) - u + C )

  • ( \int \sec(u) , du = \ln |\sec(u) + \tan(u)| + C )

  • ( \int \csc(u) , du = -\ln |\csc(u) + \cot(u)| + C )

• More Specific Integrals:

  • ( \int \sec(u) \tan(u) , du = \sec(u) + C )

  • ( \int \csc(u) \cot(u) , du = -\csc(u) + C )

Example Integrals

• Integral of a Power Function:

  • For ( n = 2 ):

  • ( \int u^2 , du = \frac{1}{3}u^3 + C )

• Logarithmic Integral:

  • ( \int ln(u) , du = u \ln(u) - u + C )

Trigonometric Integrals

• Basic Trigonometric Formulas:

  • ( \int \sin(u) , du = -\cos(u) + C )

  • ( \int \cos(u) , du = \sin(u) + C )

• Advanced Trigonometric Functions:

  • ( \int \sec(u) , du = \ln |\sec(u) + \tan(u)| + C )

  • ( \int \csc(u) , du = -\ln |\csc(u) + \cot(u)| + C )