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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 ∫.
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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)
Definite Integrals Rules: Definite Integral Boundaries: ∫ ( ) lim →. (. ) Odd Function: If ( ) = − (− ), then. = ( ) −. ( ) = lim → − ( ) −. ∫.
Contents Preface xvii 1 Areas, volumes and simple sums 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Areas of simple shapes ...
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.
CLP-2 Integral Calculus. Joel Feldman University of British Columbia Andrew Rechnitzer University of British Columbia Elyse Yeager University of British Columbia August 23, 2022. iii. CoverDesign: NickLoewen—licensedundertheCC-BY-NC-SA4.0License. Source files: A link to the source files for this document can be found at theCLP textbookwebsite.
