What is expand (xe^{ax})(e^{bx}+be^{bx}x) ?

The solution to expand (xe^{ax})(e^{bx}+be^{bx}x) is e^{bx+ax}x+be^{bx+ax}x^2

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expand (xe^{ax})(e^{bx}+be^{bx}x)

expand

(x e^{a x}) (e^{b x} + b e^{b x} x)

e^{b x + a x} x + b e^{b x + a x} x^{2}

Solution steps

(x e^{a x}) (e^{b x} + b e^{b x} x)

= (e^{a x} x) (e^{b x} + b e^{b x} x)

Apply the distributive law:

a (b + c) = ab + a c

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

= (x e^{a x}) e^{b x} + (x e^{a x}) b e^{b x} x

= e^{b x} (e^{a x} x) + b e^{b x} x (e^{a x} x)

Simplify

e^{b x} (e^{a x} x) + b e^{b x} x (e^{a x} x) : e^{b x + a x} x + b e^{b x + a x} x^{2}

= e^{b x + a x} x + b e^{b x + a x} x^{2}

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

\frac{5 x}{( 2 - x ) ( x + 4 )}

A (- 8, 3) y B (- 2, - 5)

(2 x + 1)^{3} \cdot e^{5 x}

(2 cos (x) + 1) (2 cos (3 x) - 2)

What is expand (xe^{ax})(e^{bx}+be^{bx}x) ?
The solution to expand (xe^{ax})(e^{bx}+be^{bx}x) is e^{bx+ax}x+be^{bx+ax}x^2