What is the integral from 1 to 3 of (x^3)/3+1/(4x) ?

The integral from 1 to 3 of (x^3)/3+1/(4x) is 20/3+1/4 ln(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 3 of (x^3)/3+1/(4x)

\int_{1}^{3} \frac{x ^{3}}{3} + \frac{1}{4 x} d x

\frac{20}{3} + \frac{1}{4} ln (3)

Decimal

6.94131 \dots

Solution steps

\int_{1}^{3} \frac{x ^{3}}{3} + \frac{1}{4 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} \frac{x ^{3}}{3} d x + \int_{1}^{3} \frac{1}{4 x} d x

\int_{1}^{3} \frac{x ^{3}}{3} d x = \frac{20}{3}

\int_{1}^{3} \frac{1}{4 x} d x = \frac{1}{4} ln (3)

= \frac{20}{3} + \frac{1}{4} ln (3)

\int_{0}^{1} (3 x + 4) e^{2 x} d x

\int_{- 3}^{1} 2 x - 3 d x

\int_{- 4}^{2} 8 - 2 x - x^{2} d x

\int_{- 1}^{3} 2 x^{2} - 4 x - 6 d x

\int_{0}^{9} (x + \frac{1}{2}) d x

What is the integral from 1 to 3 of (x^3)/3+1/(4x) ?
The integral from 1 to 3 of (x^3)/3+1/(4x) is 20/3+1/4 ln(3)