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

The integral from 1 to 3 of x/(x^2+1) is 1/2 ln(5)

Popular >

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

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

\frac{1}{2} ln (5)

Decimal Notation

0.80471 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{10} \frac{1}{2 u} d u

= \int_{2}^{10} \frac{1}{2 u} 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_{2}^{10} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{2}^{10}

Compute the boundaries:

ln (10) - ln (2)

= \frac{1}{2} (ln (10) - ln (2))

Simplify

= \frac{1}{2} ln (5)

\frac{d}{d x} (lo g_{8} (x + 9))

\int 13 sin^{2} (x co) s^{2} x d x

\int \frac{1}{4 e ^{- 9 x} + e ^{9 x}} d x

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

\int e^{x} 45 + e^{x} d x

What is the integral from 1 to 3 of x/(x^2+1) ?
The integral from 1 to 3 of x/(x^2+1) is 1/2 ln(5)