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

The integral from-2 to-1 of x/((x^2+2)^3) is -1/48

Popular >

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

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

- \frac{1}{48}

Decimal

- 0.02083 \dots

Solution steps

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

Apply u-substitution

: \int_{6}^{3} \frac{1}{2 u ^{3}} d u

= \int_{6}^{3} \frac{1}{2 u ^{3}} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{3}^{6} \frac{1}{2 u ^{3}} 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_{3}^{6} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{3}^{6}

= - \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{3}^{6}

Compute the boundaries:

\frac{1}{24}

= - \frac{1}{2} \cdot \frac{1}{24}

Simplify

= - \frac{1}{48}

\int_{0}^{3} 4 - x^{2} d x

\int_{0}^{1} 1 + 4 x^{2} x d x

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

\int_{0}^{1} 2 x e^{- x} d x

\int_{1}^{- 1} (9 x + 8)^{2} d x

What is the integral from-2 to-1 of x/((x^2+2)^3) ?
The integral from-2 to-1 of x/((x^2+2)^3) is -1/48