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

The integral from 2 to 3 of x/((x^2-3)^2) is 5/12

Popular >

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

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

\frac{5}{12}

Decimal Notation

0.41666 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{6} \frac{1}{2 u ^{2}} d u

= \int_{1}^{6} \frac{1}{2 u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{1}^{6} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{1}^{6}

= \frac{1}{2} [- \frac{1}{u}]_{1}^{6}

Compute the boundaries:

\frac{5}{6}

= \frac{1}{2} \cdot \frac{5}{6}

Simplify

= \frac{5}{12}

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

x y^{^{'}} - y = 2 x^{2} + 2 x + 2

\frac{d}{d x} (x + e^{x})

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

\frac{d}{d x} (\frac{1}{arccos ( 3 x )})

What is the integral from 2 to 3 of x/((x^2-3)^2) ?
The integral from 2 to 3 of x/((x^2-3)^2) is 5/12