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

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

Popular >

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

\int \frac{2 + ln ( x )}{x} d x

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

Solution steps

\int \frac{2 + ln ( x )}{x} d x

Expand

\frac{2 + ln ( x )}{x} : \frac{2}{x} + \frac{ln ( x )}{x}

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

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

Add a constant to the solution

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

\int \frac{5 x ^{2}}{x ^{3} - 2} d x

\int (\frac{3 x ^{2} + 6 x + 1}{x}) d x

\int (\frac{x ^{2}}{x - 1}) d x

\int \frac{9 x ^{3}}{x ^{3} + 1} d x

\int \frac{x}{x ^{2} - 8 x - 7} d x

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