What is expand 5(2^x+x)^4(2^xln(2)+1) ?

The solution to expand 5(2^x+x)^4(2^xln(2)+1) is

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expand 5(2^x+x)^4(2^xln(2)+1)

expand

5 (2^{x} + x)^{4} (2^{x} ln (2) + 1)

5 ln (2) \cdot 3 2^{x} + 5 ln (2) \cdot 2^{4 x + 2} x + 15 ln (2) \cdot 2^{3 x + 1} x^{2} + 5 ln (2) \cdot 2^{2 x + 2} x^{3} + 5 ln (2) \cdot 2^{x} x^{4} + 5 \cdot 1 6^{x} + 5 \cdot 2^{3 x + 2} x + 15 \cdot 2^{2 x + 1} x^{2} + 5 \cdot 2^{2 + x} x^{3} + 5 x^{4}

Solution steps

5 (2^{x} + x)^{4} (2^{x} ln (2) + 1)

= 5 (2^{x} + x)^{4} (ln (2) \cdot 2^{x} + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = 5 (2^{x} + x)^{4}, b = 2^{x} ln (2), c = 1

= 5 (2^{x} + x)^{4} \cdot 2^{x} ln (2) + 5 (2^{x} + x)^{4} \cdot 1

= 5 ln (2) \cdot 2^{x} (2^{x} + x)^{4} + 5 \cdot 1 \cdot (2^{x} + x)^{4}

Simplify

5 ln (2) \cdot 2^{x} (2^{x} + x)^{4} + 5 \cdot 1 \cdot (2^{x} + x)^{4} : 5 ln (2) \cdot 3 2^{x} + 5 ln (2) \cdot 2^{4 x + 2} x + 15 ln (2) \cdot 2^{3 x + 1} x^{2} + 5 ln (2) \cdot 2^{2 x + 2} x^{3} + 5 ln (2) \cdot 2^{x} x^{4} + 5 \cdot 1 6^{x} + 5 \cdot 2^{3 x + 2} x + 15 \cdot 2^{2 x + 1} x^{2} + 5 \cdot 2^{2 + x} x^{3} + 5 x^{4}

= 5 ln (2) \cdot 3 2^{x} + 5 ln (2) \cdot 2^{4 x + 2} x + 15 ln (2) \cdot 2^{3 x + 1} x^{2} + 5 ln (2) \cdot 2^{2 x + 2} x^{3} + 5 ln (2) \cdot 2^{x} x^{4} + 5 \cdot 1 6^{x} + 5 \cdot 2^{3 x + 2} x + 15 \cdot 2^{2 x + 1} x^{2} + 5 \cdot 2^{2 + x} x^{3} + 5 x^{4}

(- 1 + 3)^{4}

(3 x^{2} + 6 x y^{2}) d x + (6 x^{2} y + 4 y^{3}) d y

\frac{1}{( t ^{2} - 1 ) ^{2}}

(- 3, 2, - 2) y (- 2, 3, - 4)

(x + \frac{1}{2}) (x + \frac{1}{4})

What is expand 5(2^x+x)^4(2^xln(2)+1) ?
The solution to expand 5(2^x+x)^4(2^xln(2)+1) is