What is area y=(-2x^2+3x-15)/(x^3-9x),x=1,x=2 ?

The answer to area y=(-2x^2+3x-15)/(x^3-9x),x=1,x=2 is 3ln(2)-ln(5)+(28ln(2)-8ln(5))/6

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area y=(-2x^2+3x-15)/(x^3-9x),x=1,x=2

area

y = \frac{- 2 x ^{2} + 3 x - 15}{x ^{3} - 9 x}, x = 1, x = 2

3 ln (2) - ln (5) + \frac{28 ln ( 2 ) - 8 ln ( 5 )}{6}

Decimal Notation

1.55877 \dots

Solution steps

Apply the area formula:

\int_{1}^{2} \frac{- 2 x ^{2} + 3 x - 15}{∣ x ^{3} - 9 x ∣} d x

Solve

\int_{1}^{2} \frac{- 2 x ^{2} + 3 x - 15}{∣ x ^{3} - 9 x ∣} d x : 3 ln (2) - ln (5) + \frac{28 ln ( 2 ) - 8 ln ( 5 )}{6}

The area is:

= 3 ln (2) - ln (5) + \frac{28 ln ( 2 ) - 8 ln ( 5 )}{6}

\int sin (\frac{2 x}{3}) d x

\frac{d}{d x} (ln ((2 x)^{3 x}))

y = x^{2} - 3 x, (3, 0)

t (t - 4) y^{^{'}} + y = 0

x \to 2 lim (9 x^{2})

What is area y=(-2x^2+3x-15)/(x^3-9x),x=1,x=2 ?
The answer to area y=(-2x^2+3x-15)/(x^3-9x),x=1,x=2 is 3ln(2)-ln(5)+(28ln(2)-8ln(5))/6