What is the integral from 1 to 4 of (x^2+2)/(5x-x^2) ?

The integral from 1 to 4 of (x^2+2)/(5x-x^2) is 10ln(2)+(8ln(2))/5-3

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integral from 1 to 4 of (x^2+2)/(5x-x^2)

\int_{1}^{4} \frac{x ^{2} + 2}{5 x - x ^{2}} d x

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

Decimal

5.04050 \dots

Solution steps

\int_{1}^{4} \frac{x ^{2} + 2}{5 x - x ^{2}} d x

\frac{x ^{2} + 2}{5 x - x ^{2}} = \frac{5 x + 2}{5 x - x ^{2}} - 1

= \int_{1}^{4} \frac{5 x + 2}{5 x - x ^{2}} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{4} \frac{5 x + 2}{5 x - x ^{2}} d x - \int_{1}^{4} 1 d x

\int_{1}^{4} \frac{5 x + 2}{5 x - x ^{2}} d x = 10 ln (2) + \frac{8 ln ( 2 )}{5}

\int_{1}^{4} 1 d x = 3

= 10 ln (2) + \frac{8 ln ( 2 )}{5} - 3

x (25.5)

\frac{d}{d x} (x^{2} - 4 x - 2)

f (x) = \frac{4 x}{x + 2}, (2, 2)

\frac{\partial}{\partial x} (\frac{2 x + 2}{y ^{3}})

\frac{d}{d x} (5 x^{3} 25 - x^{2})

What is the integral from 1 to 4 of (x^2+2)/(5x-x^2) ?
The integral from 1 to 4 of (x^2+2)/(5x-x^2) is 10ln(2)+(8ln(2))/5-3