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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

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

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

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

6 (- e^{3 x} (2 sin (2 x) - 3 cos (2 x)))

(sec (x) + tan (x))^{3} (sec (x) - tan (x))^{4}

((cos (θ) + i sin (θ)))^{3}

c H (r (o, s, x), o, s, x) a d r (o, s, x) a d os (x - 2 x = 6)

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