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Integrals with Trigonometric Functions Z sinaxdx= 1 a cosax (63) Z sin2 axdx= x 2 sin2ax 4a (64) Z sinn axdx= 1 a cosax 2F 1 1 2; 1 n 2; 3 2;cos2 ax (65) Z sin3 axdx= 3cosax 4a + cos3ax 12a (66) Z cosaxdx=
5.2 The Definite Integral; 5.3 The Fundamental Theorem of Calculus; 5.4 Integration Formulas and the Net Change Theorem; 5.5 Substitution; 5.6 Integrals Involving Exponential and Logarithmic Functions; 5.7 Integrals Resulting in Inverse Trigonometric Functions
21 Δεκ 2020 · For this course, all work must be shown to obtain most of these integral forms. Of the integration formulas listed below, the only ones that can be applied without further work are #1 - 10, 15 - 17, and 49 and 50. And even these will require work to be shown if a substitution is involved.
7 Σεπ 2022 · Basic Integrals. 1. \(\quad \displaystyle ∫u^n\,du=\frac{u^{n+1}}{n+1}+C,\quad n≠−1\) 2. \(\quad \displaystyle ∫\frac{du}{u} =\ln |u|+C\) 3. \(\quad \displaystyle ∫e^u\,du=e^u+C\) 4. \(\quad \displaystyle ∫a^u\,du=\frac{a^u}{\ln a}+C\) 5. \(\quad \displaystyle ∫\sin u\,du=−\cos u+C\) 6. \(\quad \displaystyle ∫\cos u\,du=\sin u+C\)
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 ∫.
Table of Basic Integrals1 (1) Z xn dx = 1 n+1 xn+1; n 6= 1 (2) Z 1 x dx = lnjxj (3) Z u dv = uv Z vdu (4) Z e xdx = e (5) Z ax dx = 1 lna ax (6) Z lnxdx = xlnx x (7) Z sinxdx = cosx (8) Z cosxdx = sinx (9) Z ... CSUN, Integrals, Table of Integrals, Math 280, Math 351, Differential Equations Created Date:
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 ...
