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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 ∫.
Page 2 of 6. INTEGRATION FORMULAE STANDARD INTEGRALS 1. ∫, ( )- ( ) , ( )- [where, n ≠ 1- 2. ∫ ( ) ( ) * ( )+ 3. ∫ ( ) ∫ ( ) [where, v be the function of x]
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 ...
I can write the formula using algebra, which allows any constant speed sand any time of travel t: The distance f at constant speed s in travel time t is f Ds times t.
Section 8.1: Using Basic Integration Formulas. A Review: The basic integration formulas summarise the forms of indefinite integrals for may of the functions we have studied so far, and the substitution method helps us use the table below to evaluate more complicated functions involving these basic ones.
Basic Integration Formulas. As with differentiation, there are two types of formulas, formulas for the integrals of specific functions and structural type formulas. Each formula for the derivative of a specific function corresponds to a formula for the derivative of an elementary function.
Basic Integration Formulas 1. Power functions: (1) Z xn = xn+1 n+1 +C,n 6= −1 (2) Z 1 x dx = ln|x|+C 2. Trigonometric functions: (3) Z sinxdx = −cosx+C (4) Z cosxdx = sinx+C (5) Z sec2xdx = tanx+C (6) Z csc2 xdx = −cotx+C (7) Z secxtanxdx = secx+C (8) Z cscxcotx = −cscx+C 3. Exponential function: (9) Z exdx = ex +C 4. Inverse of ...
