`int (x^2 - 5x + 16)/((2x + 1)(x - 2)^2) dx` Evaluate the integral
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`int(x^2-5x+16)/((2x+1)(x-2)^2)dx2`
Let's first express the integrand as sum of proper rational expressions by applying partial fraction decomposition,
`(x^2-5x+16)/((2x+1)(x-2)^2)=A/(2x+1)+B/(x-2)+C/(x-2)^2`
`=(A(x-2)^2+B(2x+1)(x-2)+C(2x+1))/((2x+1)(x-2)^2)`
`=(A(x^2-4x+4)+B(2x^2-4x+x-2)+C(2x+1))/((2x+1)(x-2)^2)`
`=(A(x^2-4x+4)+B(2x^2-3x-2)+C(2x+1))/((2x+1)(x-2)^2)`
`=(x^2(A+2B)+x(-4A-3B+2C)+4A-2B+C)/((2x+1)(x-2)^2)`
Now equate the coefficients of the polynomial in the numerator on the both sides,
`A+2B=1` --------------------------------(1)
`-4A-3B+2C=-5` -----------------(2)
`4A-2B+C=16` ----------------------(3)
Now let's solve the above three equations by the...
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