What is the integral from 0 to 2 of x/((3-x)^2) ?

The integral from 0 to 2 of x/((3-x)^2) is 2-ln(3)

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integral from 0 to 2 of x/((3-x)^2)

\int_{0}^{2} \frac{x}{( 3 - x ) ^{2}} d x

2 - ln (3)

Decimal Notation

0.90138 \dots

Solution steps

\int_{0}^{2} \frac{x}{( 3 - x ) ^{2}} d x

Apply Integration By Parts

: [\frac{x}{3 - x} - \int \frac{1}{3 - x} d x]_{0}^{2}

= [\frac{x}{3 - x} - \int \frac{1}{3 - x} d x]_{0}^{2}

\int \frac{1}{3 - x} d x = - ln ∣ 3 - x ∣

= [\frac{x}{3 - x} - (- ln ∣ 3 - x ∣)]_{0}^{2}

Simplify

= [\frac{x}{3 - x} + ln ∣ 3 - x ∣]_{0}^{2}

Compute the boundaries:

2 - ln (3)

= 2 - ln (3)

\frac{4 s}{s ^{2} + 4}

y^{^{''}} - 3 y^{^{'}} - 2 y = 0

x^{5} - x^{3}

y^{^{'}} = \frac{4 x}{y}

x \to 1 lim ((x) (x - 1)^{- 1})

What is the integral from 0 to 2 of x/((3-x)^2) ?
The integral from 0 to 2 of x/((3-x)^2) is 2-ln(3)