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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 ∫.
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:
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 Integrals 1. Z [u(x)]ru0(x)dx = ur+1(x) r +1 +C, r 6=−1 2. Z u0(x) u(x) dx =ln|u(x)|+C 3. Z eu(x)u0(x)dx = eu(x) +C 4. Z sin[u(x)]u0(x)dx = −cos u(x)+C 5. Z cos[u(x)]u0(x)dx = sin u(x)+C 6. Z tan[u(x)]u0(x)dx =ln|sec u(x)|+C 7. Z cot[u(x)]u0(x)dx =ln|sin u(x)|+C 8. Z sec[u(x)]u0(x)dx =ln|sec u(x)+tanu(x)|+C 9. Z csc[u(x)]u0(x)dx ...
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. \(\quad \displaystyle ∫\cos u\,du=\sin u+C\)
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
