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Popular >

integral of ln|x|

Solution

\int ln ∣ x ∣ d x

Solution

x ln ∣ x ∣ - x + C

Solution steps

\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

Add a constant to the solution

= x ln ∣ x ∣ - x + C

Popular Examples

integral of 1/((x^2-16)^2)

\int \frac{1}{( x ^{2} - 16 ) ^{2}} d x

y^{^{'}} = y^{2}, y (0) = 2

derivative of sqrt((x^2*5^x^9))

\frac{d}{d x} ((x^{2} \cdot 5^{x})^{9})

limit as x approaches 0 of 7/x-7/(x^2-x)

x \to 0 lim (\frac{7}{x} - \frac{7}{x ^{2} - x})

xy^{''}+2y^'-4=0

x y^{^{''}} + 2 y^{^{'}} - 4 = 0

Frequently Asked Questions (FAQ)

What is the integral of ln|x| ?
The integral of ln|x| is xln|x|-x+C