Integrate (x-1)(x+1)dx / (x-2)(x-3)
Thanks for any help
2016 HSC (Accelerated)
// 2 Unit Maths // Studies of Religion 1 //
2017 HSC
// Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //
I accidentally split the numerator before I did partial fractions so I had:
x + integral (5x-7)dx/(x^2 - 5x+6)
So I split it up into:
x + integral (5/2 * (2x-5) + 11/2)/(x^2 - 5x + 6)
x + 5/2 * integral (2x-5)/(x^2 - 5x+6) + 11/2 * integral (dx/(x-3)(x-2))
x + 5/2 * ln|x^2 - 5x + 6| + 11/2 * integral (dx/(x-3)(x-2)) and then I did partial fractions on this
And got A = 1, B = -1
=> x + 5/2 * ln|x^2 - 5x + 6| + 11/2 * integral (1/(x-3) - 1/(x-2) dx
= x + 5/2 * ln|x^2 - 5x + 6| + 11/2 * ln|(x-3)/(x-2)| + C
But the answer is x - 3ln(x-2) +8ln(x-3) + C
Did I do a mistake in the working?
2016 HSC (Accelerated)
// 2 Unit Maths // Studies of Religion 1 //
2017 HSC
// Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //
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