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Page 2 of 6. INTEGRATION FORMULAE STANDARD INTEGRALS 1. ∫, ( )- ( ) , ( )- [where, n ≠ 1- 2. ∫ ( ) ( ) * ( )+ 3. ∫ ( ) ∫ ( ) [where, v be the function of x]
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 ∫.
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.
Integration by parts: u dv = uv. −. v du + C. ax + b. Partial Fractions: to integrate a function like : (x + c)(x + d) ax + b A B A(x + d) + B(x + c) Write = + = , (x + c)(x + d) (x + c) (x + d) (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 .
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.
Sometimes we can rewrite an integral to match it to a standard form. More often however, we will need more advanced techniques for solving integrals. First, let’s look at some examples of our known methods. Basic integration formulas. 1. k dx = kx + C. 2. xndx xn+1. = + C. + 1. 3. dx = ln |x| + C.
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