What is the integral of ln(x)x' ?

The integral of ln(x)x' is xln(x)x'-x+C

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integral of ln(x)x'

\int ln (x) x^{'} d x

x ln (x) x' - x + C

Solution steps

\int ln (x) x^{'} d x

Apply Integration By Parts

: x ln (x) x^{'} - \int 1 d x

= x ln (x) x^{^{'}} - \int 1 d x

\int 1 d x = x

= x ln (x) x^{^{'}} - x

Add a constant to the solution

= x ln (x) x^{^{'}} - x + C

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

n = 1 \sum \infty \frac{e ^{n}}{π ^{n}}

\frac{d}{d x} (\frac{5 ^{x^{3}}}{4 x ^{2}})

y y^{^{'}} = \frac{7}{x}

(1 + e^{2 x}) y^{2} d y = e^{x} d x, y (0) = 0