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  1. 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 ∫.

  2. Page 2 of 6. INTEGRATION FORMULAE STANDARD INTEGRALS 1. ∫, ( )- ( ) , ( )- [where, n ≠ 1- 2. ∫ ( ) ( ) * ( )+ 3. ∫ ( ) ∫ ( ) [where, v be the function of x]

  3. 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.

  4. Contents v 4.3.2 Radius of a tree trunk . . . . . . . . . . . . . . . . . . . 68 4.3.3 Birth rates and total births . . . . . . . . . . . . . . . . . 71

  5. 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. 11. csc(x) cot(x) dx = − csc(x) + C. (any number k) (n 6= −1)

  6. Differentiation Formulas d dx k = 0 (1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x ...

  7. Use the basic integration formulas to find indefinite integrals. Use substitution to find indefinite integrals. Use substitution to evaluate definite integrals. Use integration to solve real-life problems.

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