While evaluating the integral ∫x+1x2−12x+32dx using the technique of Partial Fractions, the value of A+B2

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brawnyN · Accepted Answer

Step 1 Form from rational function to partial fraction: px+q(x−a)(x−b)=Ax−a+Bx−b The given integral is: ∫x+1x2−12x+32dx Using the technique of Partial fractions, we need to find the value of A+B2 Step 2 The given integral can be rewritten as: ∫x+1x2−12x+32dx=∫1+xx2−8x−4x+32dx =∫x+1x(x−8)−4(x−8)dx =∫x+1(x−8)(x−4)dx Using the technique of Partial fractions, we get x+1(x−8)(x−4)=Ax−8+Bx−4 x+1(x−8)(x−4)=A(x−4)+B(x−8)(x−8)(x−4) x+1=A(x−4)+B(x−8) Step 3 For x=4, 4+1=A(4−4)+B(4−8) 5=A(0)+B(−4) 5=−4B −54=B For x=8, 8+1=A(8−4)+B(8−8) 9=A(4)+B(0) 9=4A 94=A The value of A is 94 and the value of B is −54. Step 4 Now, we need to find the value of A+B2 A+B2=94+(−5)42 =

While evaluating the integral \int\frac{x+1}{x^2-12x+32}dx using the techn

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