What is the integral from 1 to 2 of (4+x)/x ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of (4+x)/x

\int_{1}^{2} \frac{4 + x}{x} d x

4 ln (2) + 1

Decimal

3.77258 \dots

Solution steps

\int_{1}^{2} \frac{4 + x}{x} d x

Expand

\frac{4 + x}{x} : \frac{4}{x} + 1

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

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

\int_{1}^{2} 1 d x = 1

= 4 ln (2) + 1

\int_{- 4}^{0} \frac{3}{2} x + 6 d x

\int_{- 1}^{1} cos (w x) d x

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

\int_{0}^{1} x e^{x} - \frac{e ^{2 x}}{2} d x

\int_{- 2 π}^{2 π} (7 sin (x)) d x

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