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

The integral of (sqrt(x)+ln(x))/x is 2sqrt(x)+(ln^2(x))/2+C

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integral of (sqrt(x)+ln(x))/x

\int \frac{x + ln ( x )}{x} d x

2 x + \frac{ln ^{2} ( x )}{2} + C

Solution steps

\int \frac{x + ln ( x )}{x} d x

Expand

\frac{x + ln ( x )}{x} : \frac{1}{x} + \frac{ln ( x )}{x}

= \int \frac{1}{x} + \frac{ln ( x )}{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{1}{x} d x + \int \frac{ln ( x )}{x} d x

\int \frac{1}{x} d x = 2 x

\int \frac{ln ( x )}{x} d x = \frac{ln ^{2} ( x )}{2}

= 2 x + \frac{ln ^{2} ( x )}{2}

Add a constant to the solution

= 2 x + \frac{ln ^{2} ( x )}{2} + C

\frac{d}{d x} (\frac{a}{x ^{b}})

x \to - 4 lim (\frac{1}{x ^{2} - 16})

(1 + x^{4}) \frac{d y}{d x} = 2 x^{3} (1 - y^{2})

n = 0 \sum \infty \frac{1}{2 ^{2 n - 1}}

\int_{0}^{a} \frac{1}{( a + r - x ) ^{2}} d x

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