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Popular >

integral of ln(1/x)

Solution

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

Solution

- x ln (x) + x + C

Solution steps

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

Apply Integration By Parts

: - x ln (x) - \int - 1 d x

= - x ln (x) - \int - 1 d x

\int - 1 d x = - x

= - x ln (x) - (- x)

Simplify

= - x ln (x) + x

Add a constant to the solution

= - x ln (x) + x + C

Popular Examples

(dy)/(dt)=(a*2)-y/(20)2,y(0)=0

\frac{d y}{d t} = (a \cdot 2) - \frac{y}{20} 2, y (0) = 0

(dy)/(dx)=x(4x+5)^{1/3}

\frac{d y}{d x} = x (4 x + 5)^{\frac{1}{3}}

f(x)=sqrt(2x-x^2)

f (x) = 2 x - x^{2}

derivative of ln(x^{1/x})

\frac{d}{d x} (ln (x^{\frac{1}{x}}))

integral of (2/3 sec(x)tan(x))

\int (\frac{2}{3} sec (x) tan (x)) d x

Frequently Asked Questions (FAQ)

What is the integral of ln(1/x) ?
The integral of ln(1/x) is -xln(x)+x+C