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Integral Table from http://integral-table.com. Table of Integrals∗. Basic Forms. xndx 1 = xn+1. + 1. p 2 p. ax + bdx = ( 2b2 + abx + 3a2x2) ax + b (26) 15a2. 1 dx = ln jxj (2) x. px(ax +. = h(2ax + b)pax(ax + b) 4a3=2. p. b2 i ln a x + pa(ax + b) (27) Z. 1. b)dx. udv = uv. vdu. (3) Integrals with Logarithms. Z. ln axdx = x ln ax x. (42)
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.
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.
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
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 ...
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. \(\quad \displaystyle ∫\cos u\,du=\sin u+C\)
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