Αποτελέσματα Αναζήτησης
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. 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.
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.
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)
Integration by parts: u dv = uv − v du + C Partial Fractions: to integrate a function like ax+b (x+c)(x+d): Write ax+b (x+c)(x+d) = A (x+c) + B (x+d) = A(x+d)+B(x+c) (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 ...
This section introduces basic formulas of integration of elementary functions and the main properties of indefinite integrals. The section explains how to derive integration formulas from well-known differentiation rules.
