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Integrals of Exponential and Logarithmic Functions. ∫ ln x dx = x ln x − x + C. + 1 x. + 1. x ∫ x ln xdx = ln x − + C. 2 + 1 ( n + 1 ) x dx = e x + C ∫.
Page 2 of 6. INTEGRATION FORMULAE STANDARD INTEGRALS 1. ∫, ( )- ( ) , ( )- [where, n ≠ 1- 2. ∫ ( ) ( ) * ( )+ 3. ∫ ( ) ∫ ( ) [where, v be the function of x]
A Review: The basic integration formulas summarise the forms of indefinite integrals for may of the functions we have studied so far, and the substitution method helps us use the table below to evaluate more complicated functions involving these basic ones.
Integral formulas are listed along with the classification based on the types of functions involved. Also, get the downloadable PDF of integral formulas for different functions like trigonometric functions, rational functions, etc.
Basic Integration Formulas. As with differentiation, there are two types of formulas, formulas for the integrals of specific functions and structural type formulas. Each formula for the derivative of a specific function corresponds to a formula for the derivative of an elementary function.
Properties of the Integral: (1) Z b a f(x)dx = Z a b f(x)dx (2) Z a a f(x)dx = 0 (3) Z b a kf(x)dx = k Z b a f(x)dx (4) Z b a [f(x)+g(x)]dx = Z b a f(x)dx+ Z b a g(x)dx (5) Z b a f(x)dx = Z c a f(x)dx+ Z b c f(x)dx (a < c < b) (6) Z b a F0(x)dx = F(b) F(a) (7) d dx Z x a f(t)dt = f(x) (8) d dx Z g(x) a f(t)dt = f(g(x))g0(x) (9) d dx Z g(x) h(x ...
Write = + = , (x + c)(x + d) (x + c) (x + d) (x + c)(x + d) so ax + b = A(x + d) + B(x + c) = (A + B)x + (Ad + Bc), so a = A + B and b = Ad + Bc; solve for A and B . The approach for more general denomenator can be found in nearly any calculus textbook.
