What is expand (cos(x)+xsin(x))^2 ?

The solution to expand (cos(x)+xsin(x))^2 is x^2sin^2(x)+xsin(2x)+cos^2(x)

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expand (cos(x)+xsin(x))^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Simplify

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

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

\frac{4 x ( 14 x ^{2} - x ^{3} )}{147}

\frac{( x - 1 ) ( x + 5 )}{x - 5}

\frac{( x - y ) ^{3}}{x + y}

\frac{( x - 6 ) n ^{n}}{( n + 1 ) ^{n + 1}}

\frac{4 x ^{2} + 3}{( x - 1 ) ( x ^{2} + x + 5 )}

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