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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]
Basic integration formulas. (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.
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.
Created by T. Madas Created by T. Madas Question 7 Integrate: 1. 5 5sin2 cos2 2 ∫ x dx x C= − + 2. 1 3cos6 sin6 2 ∫ xdx x C= + 3. ∫5sin 4cos2 5cos 2sin2x x dx x x C− = − − + 4. 5 3 5cos2 3sin5 sin2 cos5 2 5 ∫ x x dx x x C− = + + 5. ∫15cos3 15sin5 5sin3 3cos5x x dx x x C− = + + 6. 1 1 1 sin8 cos3 cos8 sin3
Integration Rules and Formulas 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 =
Basic Integration Formulas. Power functions: xn+1. xn = + C, n 6= −1. + 1. 1. dx = ln |x| + C. x. 2. Trigonometric functions: Z. (3) sin xdx = − cos x + C. Z. (4) cos xdx = sin x + C. Z. (5) sec2xdx = tan x + C. Z. (6) csc2 xdx = − cot x + C. Z. (7) sec x tan xdx = sec x + C. Z. (8) csc x cot x = − csc x + C. 3. Exponential function: Z.
