What is the integral of (2sqrt(x)+5)/x ?

The integral of (2sqrt(x)+5)/x is 4sqrt(x)+5ln|x|+C

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integral of (2sqrt(x)+5)/x

\int \frac{2 x + 5}{x} d x

4 x + 5 ln ∣ x ∣ + C

Solution steps

\int \frac{2 x + 5}{x} d x

Expand

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

= \int \frac{2}{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 \frac{2}{x} d x + \int \frac{5}{x} d x

\int \frac{2}{x} d x = 4 x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= 4 x + 5 ln ∣ x ∣

Add a constant to the solution

= 4 x + 5 ln ∣ x ∣ + C

\int_{0}^{16} x 16 - x d x

\int_{0}^{\infty} \frac{x}{x ^{3} + 1} d x

x \to 3 lim (\frac{4 x - 5}{5 x - 1})

\int + x^{2} x^{3} + 27 d x

\frac{2 s e ^{- 3 s}}{3 s ^{2} + 27}

What is the integral of (2sqrt(x)+5)/x ?
The integral of (2sqrt(x)+5)/x is 4sqrt(x)+5ln|x|+C