83-86. Repeated quadratic factors Refer to the summary box (Partial Fraction Decompositions) and evaluate the following integrals. 83. dx x(x? + 1)2 dx 84. I (x + 1)(x² + 2x + 2)² 85. |x – 1)(x² + 2x + 2)²* x' + 1 x(x? + x + 1)2 86.

Q: 4x4 + 14x² + 2 3. Evaluate -dx using partial fractions. 4x4 + x²

A: By partial fraction method

Q: M 6. Use Partial Fractions to determine the e 5 cx = (A₂+B А dx x-3 X+2 1 (x-3)(x+2)

A:

Q: or f (x) = e-*+3, find f'(2.5). %3D

A: Given query is to find indicated derivative.

Q: 3x? +5x –13 3. Express in partial fraction term. 3x+2 x? - 4x +4

A: Partial fractions

Q: 4. Use the method of partial fractions to evaluate 6x2 -10x+ 3 dx x' - 3x

A:

Q: 1. 5x+7 ܐ ] x3+ 2x – x =2 dx

A:

Q: 8x2 -7x +1 Find the partial fraction decomposition of- x³ - 2x2 + x

A: Solution: Perform the partial fraction decomposition of 8x2-7x+18x3-2x2+x Simplify the expression…

Q: 18dx ·S (4x² +9) 19.

A:

Q: Write the rational function as a sum of partial fractions: x+1 A B -- A = J.B = + (x-4)(x+7)¯ x-4…

A: Given that, x+1x-4x+7=Ax-4+Bx+7  ----(1) To find A and B, Taking least common divisor on the right…

Q: xdx x² - 4x (x+2XX-2

A:

Q: 6х3 + х2— 5х —7 –dx. Use Зx2 —х — 2

A: