What is expand e^x(ln(x)+1/x) ?

The solution to expand e^x(ln(x)+1/x) is e^xln(x)+(e^x)/x

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expand e^x(ln(x)+1/x)

expand

e^{x} (ln (x) + \frac{1}{x})

e^{x} ln (x) + \frac{e ^{x}}{x}

Solution steps

e^{x} (ln (x) + \frac{1}{x})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x}, b = ln (x), c = \frac{1}{x}

= e^{x} ln (x) + e^{x} \frac{1}{x}

e^{x} \frac{1}{x} = \frac{e ^{x}}{x}

= e^{x} ln (x) + \frac{e ^{x}}{x}

(3 x^{2} - \frac{1}{x})^{15}

\frac{2 x ^{3} - 4 x ^{2} - 12 x + 3}{( x - 1 ) ^{2}}

\frac{x + 11}{( x - 2 ) ( x + 7 )}

(- 2 + \frac{i - 1}{n})^{3}

(3 - x + 1)^{2}

What is expand e^x(ln(x)+1/x) ?
The solution to expand e^x(ln(x)+1/x) is e^xln(x)+(e^x)/x