Αποτελέσματα Αναζήτησης
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=
Integral formulas are listed along with the classification based on the types of functions involved. Also, get the downloadable PDF of integral formulas for different functions like trigonometric functions, rational functions, etc.
Integrals of Trigonometric Functions. ∫ sin x dx = − cos x + C. ∫ cos x dx = sin x + C. ∫ tan x dx = ln sec x + C. ∫ sec x dx = ln tan x + sec x + C. ∫ 1. sin. 2. x dx = ( x − sin x cos x ) + C.
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) x(x + a)ndx = (n + 1)(n + 2) (8) 1 dx. + x2 = tan 1 x.
1.1 Review of Functions; 1.2 Basic Classes of Functions; 1.3 Trigonometric Functions; 1.4 Inverse Functions; 1.5 Exponential and Logarithmic Functions
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 ...
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 ...
