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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=
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 ∫.
Integral Table from http://integral-table.com. Table of Basic Integrals. Basic Forms. 1 xndx = xn+1; n 6= 1. + 1. 1 dx. = ln jxj. Z. udv = uv. Z. vdu. (4) Z 1 1 dx = ln jax + bj ax + b a. Integrals of Rational Functions. (5) Z 1 1 dx = (x + a)2 x + a. (6) Z (x + a)n+1. (x + a)ndx = ; n 6= 1. n + 1. (7) Z (x + a)n+1((n + 1)x a)
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:
Definite Integral Boundaries. \int_ {a}^ {b}f (x)dx=F (b)-F (a) =\lim_ {x\to b-} (F (x))-\lim _ {x\to a+} (F (x)) Odd function \mathrm {If}\:f\left (x\right)=-f\left (-x\right)\Rightarrow\int _ {-a}^ {a}f (x)dx=0. Undefined points.
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. \(\quad \displaystyle ∫\cos u\,du=\sin u+C\)
Below is a table of Indefinite Integrals. With this table and integration techniques, you will be able to find majority of integrals.
