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

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

Popular >

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

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

\frac{1}{48}

Solution steps

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

Apply u-substitution

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

= \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}^{1} 1 - z

\int_{0}^{1} e^{1 - 3 t} d t

\int_{0}^{2} x^{2} - (4 x - x^{2}) d x

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

\int_{0}^{2} x^{4} ln (2 x) d x

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