Tolong dibantu kakk

Tolong dibantu kakk

Jawaban Terkonfirmasi

Jawaban:

dgn cara integral rasional:

$frac{x - 7}{ {x}^{2} - x - 12 }$

$= frac{x - 7}{(x - 4)(x + 3)}$

$mis. : frac{x - 7}{(x - 4)(x + 3)} = frac{a}{x - 4} + frac{b}{x + 3}$

$frac{x - 7}{(x - 4)(x + 3)} = frac{a(x + 3) + b(x - 4)}{(x - 4)(x + 3)}$

$frac{x - 7}{(x - 4)(x + 3)} = frac{(a + b)x+ (3a - 4b)}{(x - 4)(x + 3)}$

setarakan ruas kiri & ruas kanan, maka:

a+b = 1 <=> 3a + 3b = 3

3a-4b = -7 <=> 3a – 4b = -7

——————– (-)

7b = 10

b = 10/7

a = -3/7

$int( frac{x - 7}{(x - 4)(x + 3)} )=int( frac{ - frac{3}{7} }{x - 4}) + int( frac{ frac{10}{7} }{x + 3} )$

$= - frac{ 3}{7} int( frac{1}{x - 4} )+ frac{10}{7} int( frac{1}{x + 3} )$

$= - frac{ 3}{7} ln(x - 4 )+ frac{10}{7} ln(x + 3) + c$