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

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

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

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

3 + ln (2)

Decimal Notation

3.69314 \dots

Solution steps

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

Take the constant out:

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

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

Expand

\frac{2 x + 1}{x} : 2 + \frac{1}{x}

= \frac{1}{2} \cdot \int_{1}^{4} 2 + \frac{1}{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

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

\int_{1}^{4} 2 d x = 6

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

= \frac{1}{2} (6 + 2 ln (2))

Simplify

\frac{1}{2} (6 + 2 ln (2)) : 3 + ln (2)

= 3 + ln (2)

\frac{d}{d x} (x + 4)

\frac{\partial}{\partial x} (x arctan (\frac{x}{y}))

x \to \infty lim (x + x^{3})

\int e^{- s^{2}} d s

h \to 0 lim (\frac{2. 7 ^{h} - 1}{h})

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