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

The integral from 1 to 4 of (-x+4/x) is -15/2+8ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 4 of (-x+4/x)

\int_{1}^{4} (- x + \frac{4}{x}) d x

- \frac{15}{2} + 8 ln (2)

Decimal

- 1.95482 \dots

Solution steps

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

\int_{1}^{4} x d x = \frac{15}{2}

\int_{1}^{4} \frac{4}{x} d x = 8 ln (2)

= - \frac{15}{2} + 8 ln (2)

\int_{1}^{10} \frac{5}{x} d x

\int_{0}^{2} (x^{2} - 10 x + 16) d x

\int_{0}^{\infty} 2 e^{- 2 y} d y

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

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

What is the integral from 1 to 4 of (-x+4/x) ?
The integral from 1 to 4 of (-x+4/x) is -15/2+8ln(2)