What is the integral from 1 to 3 of (x^2+2)/(4x-x^2) ?

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

Popular >

integral from 1 to 3 of (x^2+2)/(4x-x^2)

\int_{1}^{3} \frac{x ^{2} + 2}{4 x - x ^{2}} d x

5 ln (3) - 2

Decimal

3.49306 \dots

Solution steps

\int_{1}^{3} \frac{x ^{2} + 2}{4 x - x ^{2}} d x

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

= \int_{1}^{3} \frac{4 x + 2}{4 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}^{3} \frac{4 x + 2}{4 x - x ^{2}} d x - \int_{1}^{3} 1 d x

\int_{1}^{3} \frac{4 x + 2}{4 x - x ^{2}} d x = 5 ln (3)

\int_{1}^{3} 1 d x = 2

= 5 ln (3) - 2

\int \frac{3 x ^{2}}{x ^{3} + 1} d x

y (x - b) + y^{^{'}} b x = 0

y^{^{'}} = \frac{- y ^{3} + 14 x - 8}{3 x y ^{2}}

\frac{d}{d x} (\frac{2}{2 x ^{4} - 5})

\frac{d}{d x} (\frac{( x + 1 ) ^{2} + ( x - 1 ) ^{2}}{x ^{2}})

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