integration formulas

Integration of Exponential and log functions 1. Integral of the exponential function $$ \int e^x \ dx=e^x + C $$ 2. Integral of the exponential function with base a $$…

Integration of Hyperbolic functions 1. Integral involving hyperbolic sine ∫sinhx dx=coshx+C 2. Integral involving hyperbolic cosine ∫coshx dx=sinhx+C 3. Integral involving hyperbolic tangent ∫tanhx dx=lncoshx+C 4. Integral involving hyperbolic cotangent ∫cothx dx=ln|sinhx|+C 5. Integral…

  Definite Integration Integrands: f, g, u, v Antiderivatives: F, G Independent variables: x, t Limits of integration: a, b, c, d Subintervals of integration: Δxi Arbitrary point of a…

Triple Integration Functions of three variables: f(x,y,z), g(x,y,z), f(u,v,w) Independent variables: x, y, z, u, v, w Small changes: Δxi, Δyj, Δzk Limits of integration: a, b, c, d, r,…

Double integration Functions of two variables: f(x,y), f(u,v), g(x,y) Independent variables: x, y, u, v Small changes: Δxi, Δyi Regions of integration: R, S Real numbers: a, b, c, d,…

Integration of inverse trigonometric functions $$ 1. \ \int \sin^{-1}x \ dx = x \sin^{-1}x + \sqrt {1-x^2} +C $$ $$ 2. \ \int \cos^{-1}x \ dx = x \cos^{-1}x…

Integration of Trigonometric functions $$ 1. \ \int \cos x \ dx = \sin x+C $$ $$ 2. \ \int \sin x \ dx=- \cos x +C $$ $$ 3.…

Integration of rational functions A function or fraction is called rational if it is represented as a ratio of two polynomials. A rational function is called proper if the degree…

Properties of Integration $$ 1. \ \int f(x)dx=F(x)+c $$ $$ 2. \ \int af(x)dx=a \int f(x)dx $$ $$ 3. \ \int \left[ f(x)+g(x) \right] dx= \int f(x)dx + \int g(x)dx…

Introduction In mathematics, when we cannot perform general addition operations, we use integration to add values on a large scale. There are various methods in mathematics to integrate functions. Just…