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 ∫.
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) 6. sin(x) dx = − cos(x) + C. 7. cos(x) dx = sin(x) + C. 8. sec2(x) dx = tan(x) + C. 9. csc2(x) dx = − cot(x) + C. 10. sec(x) tan(x) dx = sec(x) + C.
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. 2. xndx xn+1. = + C. + 1. 3. dx = ln |x| + C.
This chapter contains the fundamental theory of integration. We begin with some problems to motivate the main idea: approximation by a sum of slices. The chapter confronts this squarely, and Chapter 13 concentrates on the basic rules of calculus that you use after you have found the integrand.
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.
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.
Integration Formulas: xp+1. xp dx = + C; p 6=. + 1. (2) sin(x) dx = cos(x) + C. Z. (3) cos(x) dx = sin(x) + C. Z.
