What is expand x(Ax+B)cos(x)+x(Cx+D)sin(x) ?

The solution to expand x(Ax+B)cos(x)+x(Cx+D)sin(x) is Ax^2cos(x)+Bxcos(x)+x^2Csin(x)+Dxsin(x)

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expand x(Ax+B)cos(x)+x(Cx+D)sin(x)

expand

x (A x + B) cos (x) + x (C x + D) sin (x)

A x^{2} cos (x) + B x cos (x) + x^{2} C sin (x) + D x sin (x)

Solution steps

x (A x + B) cos (x) + x (C x + D) sin (x)

= x cos (x) (A x + B) + x sin (x) (C x + D)

Expand

x cos (x) (A x + B) : A x^{2} cos (x) + B x cos (x)

= A x^{2} cos (x) + B x cos (x) + x sin (x) (C x + D)

Expand

x sin (x) (C x + D) : x^{2} C sin (x) + D x sin (x)

= A x^{2} cos (x) + B x cos (x) + x^{2} C sin (x) + D x sin (x)

\frac{7 x ( 16 x ^{2} - x ^{3} )}{24}

(1 - cos^{2} (x))^{4}

15 x yz (\frac{x ^{2} y z ^{3}}{3} + x^{4} y^{4} z - \frac{5 x}{3 z ^{3}})

\frac{1}{2} (1 - cos (x))

(5 x + 2 y = 8,) (2 x - 4 y = - 8)

What is expand x(Ax+B)cos(x)+x(Cx+D)sin(x) ?
The solution to expand x(Ax+B)cos(x)+x(Cx+D)sin(x) is Ax^2cos(x)+Bxcos(x)+x^2Csin(x)+Dxsin(x)