What is (x-yln(y)+yln(x))dx+x(ln(y)-ln(x)) ?

The solution to (x-yln(y)+yln(x))dx+x(ln(y)-ln(x)) is (x-yln(y)+yln(x))dx+xln(y/x)

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simplify (x-yln(y)+yln(x))dx+x(ln(y)-ln(x))

simplify

(x - y ln (y) + y ln (x)) d x + x (ln (y) - ln (x))

(x - y ln (y) + y ln (x)) d x + x ln (\frac{y}{x})

Solution steps

(x - y ln (y) + y ln (x)) d x + x (ln (y) - ln (x))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (y) - ln (x) = ln (\frac{y}{x})

= (x - y ln (y) + y ln (x)) d x + x ln (\frac{y}{x})

lo g_{10} (\frac{y ^{2} x}{3 z})

4 lo g_{10} (x) - \frac{1}{4} lo g_{10} (x^{2} + 1) + 3 lo g_{10} (x - 1)

lo g_{10} (2 x^{n})

lo g_{c} (m) - lo g_{c} (n) - lo g_{c} (f)

lo g_{10} (\frac{a ^{3} b ^{2}}{c ^{3}})

What is (x-yln(y)+yln(x))dx+x(ln(y)-ln(x)) ?
The solution to (x-yln(y)+yln(x))dx+x(ln(y)-ln(x)) is (x-yln(y)+yln(x))dx+xln(y/x)