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Popular >

integral of (x+5)/x

Solution

\int \frac{x + 5}{x} d x

Solution

x + 5 ln ∣ x ∣ + C

Solution steps

\int \frac{x + 5}{x} d x

Expand

\frac{x + 5}{x} : 1 + \frac{5}{x}

= \int 1 + \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 d x + \int \frac{5}{x} d x

\int 1 d x = x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= x + 5 ln ∣ x ∣

Add a constant to the solution

= x + 5 ln ∣ x ∣ + C

Graph

Popular Examples

derivative of 1/3 sin(x)

\frac{d}{d x} (\frac{1}{3} sin (x))

derivative of f(x)=(3/5 x)^9 derivative of

f (x) = (\frac{3}{5} x)^{9}

derivative of (21/(64x^{11/4)})

\frac{d}{d x} (\frac{21}{64 x ^{\frac{11}{4}}})

integral from 0 to 1 of x^2((2(x+1))/3)

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

limit as x approaches pi-of ln(x)

x \to π - lim (ln (x))

Frequently Asked Questions (FAQ)

What is the integral of (x+5)/x ?
The integral of (x+5)/x is x+5ln|x|+C