What is the integral of-ln|x| ?

The integral of-ln|x| is -xln|x|+x+C

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integral of-ln|x|

\int - ln ∣ x ∣ d x

- x ln ∣ x ∣ + x + C

Solution steps

\int - ln ∣ x ∣ d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int ln ∣ 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

\int_{0}^{1} \int x e^{x} d x d x

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

\frac{d}{d x} (x + \frac{25}{x})

(ln (\frac{x ( x ^{2} + 1 ) ^{2}}{2 x ^{3} - 1}))^{^{'}}

f (x) = 1 + sin (x), at x = - π