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

The integral from 2 to 3 of (x^2+1)/(x^3+3x) is 1/3 ln(18/7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{3} ln (\frac{18}{7})

Decimal Notation

0.31482 \dots

Solution steps

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

Apply u-substitution

: \int_{14}^{36} \frac{1}{3 u} d u

= \int_{14}^{36} \frac{1}{3 u} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{14}^{36} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{14}^{36}

Compute the boundaries:

2 ln (6) - ln (14)

= \frac{1}{3} (2 ln (6) - ln (14))

Simplify

= \frac{1}{3} ln (\frac{18}{7})

\int_{0}^{5} \frac{x}{x - 2} d x

\int 3 x sec^{2} (4) x^{2} d x

\frac{d x}{d t} = r x

- cos (π y) d x

\int (3 x^{2} - 1) e^{x^{3} - x} d x

What is the integral from 2 to 3 of (x^2+1)/(x^3+3x) ?
The integral from 2 to 3 of (x^2+1)/(x^3+3x) is 1/3 ln(18/7)