What is expand e^xcos(x)(e^xsin(x)+cos(x)e^x) ?

The solution to expand e^xcos(x)(e^xsin(x)+cos(x)e^x) is e^{2x}cos(x)sin(x)+e^{2x}cos^2(x)

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expand e^xcos(x)(e^xsin(x)+cos(x)e^x)

expand

e^{x} cos (x) (e^{x} sin (x) + cos (x) e^{x})

e^{2 x} cos (x) sin (x) + e^{2 x} cos^{2} (x)

Solution steps

e^{x} cos (x) (e^{x} sin (x) + cos (x) e^{x})

= e^{x} cos (x) (e^{x} sin (x) + e^{x} cos (x))

Apply the distributive law:

a (b + c) = ab + a c

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

= e^{x} cos (x) e^{x} sin (x) + e^{x} cos (x) cos (x) e^{x}

= e^{x} e^{x} cos (x) sin (x) + e^{x} e^{x} cos (x) cos (x)

Simplify

e^{x} e^{x} cos (x) sin (x) + e^{x} e^{x} cos (x) cos (x) : e^{2 x} cos (x) sin (x) + e^{2 x} cos^{2} (x)

= e^{2 x} cos (x) sin (x) + e^{2 x} cos^{2} (x)

(2 x + 3)^{2}

(t^{2} - e^{3 t}) U (t - 2)

1 - \frac{1}{2} + \frac{3}{32} (4 (0.7) - \frac{0. 7 ^{3}}{3})

4 cos (t - 2) u (t - 2)

t + z (cos (t)) d t + (sin (t) - 3 z^{2} + 5) d z

What is expand e^xcos(x)(e^xsin(x)+cos(x)e^x) ?
The solution to expand e^xcos(x)(e^xsin(x)+cos(x)e^x) is e^{2x}cos(x)sin(x)+e^{2x}cos^2(x)