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

The integral from 1 to 3 of ((x^2+5))/x is 4+5ln(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^2+5))/x

\int_{1}^{3} \frac{( x ^{2} + 5 )}{x} d x

4 + 5 ln (3)

Decimal

9.49306 \dots

Solution steps

\int_{1}^{3} \frac{x ^{2} + 5}{x} d x

Expand

\frac{x ^{2} + 5}{x} : x + \frac{5}{x}

= \int_{1}^{3} x + \frac{5}{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} x d x + \int_{1}^{3} \frac{5}{x} d x

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

\int_{1}^{3} \frac{5}{x} d x = 5 ln (3)

= 4 + 5 ln (3)

\int_{4}^{7} x ln (ln (x)) d x

\int_{0}^{1} x cos (2 x) d x

\int_{x - 2}^{x + 2} \frac{3}{220} y d y

\int_{l n (5)}^{l n (7)} e^{- x} d x

\int_{0}^{c} x (c - x) d x

What is the integral from 1 to 3 of ((x^2+5))/x ?
The integral from 1 to 3 of ((x^2+5))/x is 4+5ln(3)