What is expand (sin(y))(x+sin(y))dx ?

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

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expand (sin(y))(x+sin(y))dx

expand

(sin (y)) (x + sin (y)) d x

x sin (y) d x + sin^{2} (y) d x

Solution steps

(sin (y)) (x + sin (y)) d x

Apply the distributive law:

a (b + c) = ab + a c

a = (sin (y)) d x, b = x, c = sin (y)

= (sin (y)) d xx + (sin (y)) d x sin (y)

= x (sin (y)) d x + (sin (y)) sin (y) d x

Simplify

x (sin (y)) d x + (sin (y)) sin (y) d x : x sin (y) d x + sin^{2} (y) d x

= x sin (y) d x + sin^{2} (y) d x

2 (e^{- x^{2}} - 2 e^{- x^{2}} x^{2})

\frac{1}{( 1 - k v ) ( 1 + k v )}

d x (x^{2} - 6)

\frac{y ^{2} ( y + 1 )}{x ^{2} ( x - 1 )}

(1 + sin (a))^{2}

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