What is the integral from sqrt(2) to 2 of u/(u^2-1) ?

The integral from sqrt(2) to 2 of u/(u^2-1) is 1/2 ln(3)

Popular >

integral from sqrt(2) to 2 of u/(u^2-1)

\int_{2}^{2} \frac{u}{u ^{2} - 1} d u

\frac{1}{2} ln (3)

Decimal Notation

0.54930 \dots

Solution steps

\int_{2}^{2} \frac{u}{u ^{2} - 1} d u

Apply u-substitution

: \int_{1}^{3} \frac{1}{2 v} d v

= \int_{1}^{3} \frac{1}{2 v} d v

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{3} \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{2} [ln ∣ v ∣]_{1}^{3}

Compute the boundaries:

ln (3)

= \frac{1}{2} ln (3)

\frac{\partial}{\partial y} (e^{x + y + 1})

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

y = x^{2} + 2 x + 1, y = 2 x + 5

\frac{\partial}{\partial x} (- 6 x y)

\frac{d}{d x} (\frac{1}{5} x^{5} + \frac{1}{12 x ^{3}})

What is the integral from sqrt(2) to 2 of u/(u^2-1) ?
The integral from sqrt(2) to 2 of u/(u^2-1) is 1/2 ln(3)