Αποτελέσματα Αναζήτησης
In the following example, we use the previous properties and the table of the basic integration rules to evaluate some indefinite integrals. Example 1.5 Evaluate the integral. (1)
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
Integrals with Trigonometric Functions (71) Z sinaxdx= 1 a cosax (72) Z sin2 axdx= x 2 sin2ax 4a (73) Z sin3 axdx= 3cosax 4a + cos3ax 12a (74) Z sinn axdx= 1 a cosax 2F 1 1 2; 1 n 2; 3 2;cos2 ax (75) Z cosaxdx= 1 a sinax (76) Z cos2 axdx= x 2 + sin2ax 4a (77) Z cos3 axdx= 3sinax 4a + sin3ax 12a 8
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 tanxdx = lnjsecxj (10) Z secxdx = lnjsecx+tanxj (11) Z sec2 xdx = tanx (12) Z secxtanxdx = secx (13) Z a a2 +x2 dx = tan 1 x a (14) Z a a2 ...
Engineers usually refer to a table of integrals when performing calculations involving integration. This leaflet provides such a table. Sometimes restrictions need to be placed on the values of some of the variables. These restrictions are shown in the third column. 1. A table of integrals. 1.
Integral Table To save space (and ink), only one member of each antiderivative family appears for most integrals below; for example, you should interpretZ cos(x)dx = sin(x) as Z cos(x)dx = sin(x)+C, where C is an arbi-trary constant. Basic Patterns Z k f(x)dx = k Z f(x)dx Z F0(ax +b)dx) = 1 a F(x) Z F0(g(x))g0(x)dx) = F(g(x)) Z [f(x) g(x)] dx ...
