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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 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.
Integration Formulas can be used for algebraic expressions, trigonometric ratios, inverse trigonometric functions, rational functions and for all other functions. Understand the integration formulas with examples and FAQs.
Integrals of Hyperbolic Functions Z coshaxdx= 1 a sinhax (110) Z eax coshbxdx= 8 >< >: eax a2 b2 [ acosh bx bsinh ] 6= e2ax 4a + x 2 a= b (111) Z sinhaxdx= 1 a coshax (112) eax sinhbxdx= 8 >< >: eax a2 b2 [ bcoshbx+ asinhbx] a6= b e2ax 4a x 2 a= b (113) Z eax tanhbxdx= 8 >> >> >< >> >> >: e(a+2b)x (a+ 2b)2 F 1 h 1 + a 2b;1 2 + a 2b e2bx i 1 a ...
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 ...
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)
First, let’s look at some examples of our known methods. Basic integration formulas. 1. k dx = kx + C. xn+1. 2. xndx = + C. + 1. 3. dx = ln |x| + C. x. 4. ex dx = ex + C. 5. axdx ax. = + C ln(a) 6. sin(x) dx = − cos(x) + C. 7. cos(x) dx = sin(x) + C. 8. sec2(x) dx = tan(x) + C. 9. csc2(x) dx = − cot(x) + C. 10. sec(x) tan(x) dx = sec(x) + C.
