What is the integral of (ln(x)+10)/x ?

The integral of (ln(x)+10)/x is (ln^2(x))/2+10ln|x|+C

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integral of (ln(x)+10)/x

\int \frac{ln ( x ) + 10}{x} d x

\frac{ln ^{2} ( x )}{2} + 10 ln ∣ x ∣ + C

Solution steps

\int \frac{ln ( x ) + 10}{x} d x

Expand

\frac{ln ( x ) + 10}{x} : \frac{ln ( x )}{x} + \frac{10}{x}

= \int \frac{ln ( x )}{x} + \frac{10}{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{ln ( x )}{x} d x + \int \frac{10}{x} d x

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

\int \frac{10}{x} d x = 10 ln ∣ x ∣

= \frac{ln ^{2} ( x )}{2} + 10 ln ∣ x ∣

Add a constant to the solution

= \frac{ln ^{2} ( x )}{2} + 10 ln ∣ x ∣ + C

5 - x^{2}

\int_{- 2}^{2} \frac{1}{v} d v

x \to 0 + lim (x^{5 x})

y^{^{''}} - 9 y^{^{'}} + 18 y = e^{e^{- 3 x}}

\int - sin (- x + 2) d x

What is the integral of (ln(x)+10)/x ?
The integral of (ln(x)+10)/x is (ln^2(x))/2+10ln|x|+C