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

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}

\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)

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)