What is expand x^{2x+1}(2ln(x)+(2x+1)/x) ?

The solution to expand x^{2x+1}(2ln(x)+(2x+1)/x) is 2x^{2x+1}ln(x)+2x^{1+2x}+x^{2x}

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expand x^{2x+1}(2ln(x)+(2x+1)/x)

expand

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

2 x^{2 x + 1} ln (x) + 2 x^{1 + 2 x} + x^{2 x}

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = x^{2 x + 1}, b = 2 ln (x), c = \frac{2 x + 1}{x}

= x^{2 x + 1} \cdot 2 ln (x) + x^{2 x + 1} \frac{2 x + 1}{x}

= 2 x^{2 x + 1} ln (x) + \frac{2 x + 1}{x} x^{2 x + 1}

\frac{2 x + 1}{x} x^{2 x + 1} = 2 x^{1 + 2 x} + x^{2 x}

= 2 x^{2 x + 1} ln (x) + 2 x^{1 + 2 x} + x^{2 x}

e^{i (\frac{x}{2} + 5)}

\frac{2 ( 2 x + 12 )}{3 ( 3 x + 8 )}

(2 e^{3 x} + 1)^{3}

\frac{3}{4} (16 x - 12)

What is expand x^{2x+1}(2ln(x)+(2x+1)/x) ?
The solution to expand x^{2x+1}(2ln(x)+(2x+1)/x) is 2x^{2x+1}ln(x)+2x^{1+2x}+x^{2x}