What is expand (2ln(x))(2e^x-sin(x)) ?

The solution to expand (2ln(x))(2e^x-sin(x)) is 4e^xln(x)-2sin(x)ln(x)

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expand (2ln(x))(2e^x-sin(x))

expand

(2 ln (x)) (2 e^{x} - sin (x))

4 e^{x} ln (x) - 2 sin (x) ln (x)

Solution steps

(2 ln (x)) (2 e^{x} - sin (x))

Apply the distributive law:

a (b - c) = ab - a c

a = (2 ln (x)), b = 2 e^{x}, c = sin (x)

= (2 ln (x)) \cdot 2 e^{x} - (2 ln (x)) sin (x)

= 2 e^{x} (2 ln (x)) - sin (x) (2 ln (x))

Simplify

2 e^{x} (2 ln (x)) - sin (x) (2 ln (x)) : 4 e^{x} ln (x) - 2 sin (x) ln (x)

= 4 e^{x} ln (x) - 2 sin (x) ln (x)

- \frac{8 ( - 3 s ^{2} + 18 s - 11 )}{( s ^{2} - 6 s + 25 ) ^{3}}

(x^{10} + lo g_{12} (x))^{2}

\frac{2 ( π + 180 )}{360}

(a - a cos (x))^{2}

\frac{1}{s ( s + 4 )}

What is expand (2ln(x))(2e^x-sin(x)) ?
The solution to expand (2ln(x))(2e^x-sin(x)) is 4e^xln(x)-2sin(x)ln(x)