What is expand x^3*e^{3x^2}(6x+1) ?

The solution to expand x^3*e^{3x^2}(6x+1) is 6e^{3x^2}x^4+e^{3x^2}x^3

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expand x^3*e^{3x^2}(6x+1)

expand

x^{3} \cdot e^{3 x^{2}} (6 x + 1)

6 e^{3 x^{2}} x^{4} + e^{3 x^{2}} x^{3}

Solution steps

x^{3} e^{3 x^{2}} (6 x + 1)

= e^{3 x^{2}} x^{3} (6 x + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = x^{3} e^{3 x^{2}}, b = 6 x, c = 1

= x^{3} e^{3 x^{2}} \cdot 6 x + x^{3} e^{3 x^{2}} \cdot 1

= 6 e^{3 x^{2}} x^{3} x + 1 \cdot e^{3 x^{2}} x^{3}

Simplify

6 e^{3 x^{2}} x^{3} x + 1 \cdot e^{3 x^{2}} x^{3} : 6 e^{3 x^{2}} x^{4} + e^{3 x^{2}} x^{3}

= 6 e^{3 x^{2}} x^{4} + e^{3 x^{2}} x^{3}

\frac{20 ( s + 1.5 )}{s ( s + 0.5 ) ( s + 10 )}

x (- \frac{x}{20} + 300)

\frac{9 ( 2 - 2 )}{2}

(1 + tan (α) tan (β)) tan (α + β)

(- x - 3) (- x + 3)

What is expand x^3*e^{3x^2}(6x+1) ?
The solution to expand x^3*e^{3x^2}(6x+1) is 6e^{3x^2}x^4+e^{3x^2}x^3