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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]
Sometimes we can rewrite an integral to match it to a standard form. More often however, we will need more advanced techniques for solving integrals. First, let’s look at some examples of our known methods. Basic integration formulas. 1. k dx = kx + C. xn+1. 2. xndx = + C. + 1. 3. dx = ln |x| + C. x. 4. ex dx = ex + C. 5. axdx ax. = + C ln(a)
Differentiation Formulas d dx k = 0 (1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x ...
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. Antiderivatives. Definition 1 (Antiderivative). If F0(x) = f(x) we call F an antideriv- ative of f. Definition 2R (Indefinite Integral). If F is an antiderivative of f, then f(x)dx = F(x) + c is called the (general) Indefinite Integral of f, where c is an arbitrary constant. The indefinite integral of a function ...
