Given that int_4^6 (2x^2-9x-6)/(x(x^2-x-6))dx=ln m/n, determine the values for the integers m and n.

ajumbaretu

ajumbaretu

Answered question

2022-11-18

Expressing 2 x 2 9 x 6 x ( x 2 x 6 ) in partial fraction would give you: 16 5 ( x + 2 )
Given that 4 6 2 x 2 9 x 6 x ( x 2 x 6 ) d x = l n m n , determine the values for the integers m and n.

Answer & Explanation

Aedan Hatfield

Aedan Hatfield

Beginner2022-11-19Added 16 answers

It turns out the partial fraction decomposition is incorrect.
It can be verified that instead,
4 6 2 x 2 9 x 6 x ( x 2 x 6 ) d x = 4 6 1 x + 2 x + 2 1 x 3 d x = [ ln x + 2 ln ( x + 2 ) ln ( x 3 ) ] 4 6 = ln 6 4 + 2 ln 8 6 ln 3 1 = ln 3 2 + ln 16 9 ln 3 = ln 8 9

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