What is expand e^{2x}(acos(5x)+bsin(5x)) ?

The solution to expand e^{2x}(acos(5x)+bsin(5x)) is ae^{2x}cos(5x)+be^{2x}sin(5x)

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expand e^{2x}(acos(5x)+bsin(5x))

expand

e^{2 x} (a cos (5 x) + b sin (5 x))

a e^{2 x} cos (5 x) + b e^{2 x} sin (5 x)

Solution steps

e^{2 x} (a cos (5 x) + b sin (5 x))

Apply the distributive law:

a (b + c) = ab + a c

a = e^{2 x}, b = a cos (5 x), c = b sin (5 x)

= e^{2 x} a cos (5 x) + e^{2 x} b sin (5 x)

= a e^{2 x} cos (5 x) + b e^{2 x} sin (5 x)

\frac{x + 8}{x ( x + 2 )}

\frac{\partial}{\partial x} ((y) (y^{5} - 3 x y))

\frac{5 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

(u + v) d u

15 (\frac{2}{5} - 3 x)

What is expand e^{2x}(acos(5x)+bsin(5x)) ?
The solution to expand e^{2x}(acos(5x)+bsin(5x)) is ae^{2x}cos(5x)+be^{2x}sin(5x)