What is the integral of (cos(2y)-3x^2y^2) ?

The integral of (cos(2y)-3x^2y^2) is cos(2y)x-y^2x^3+C

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integral of (cos(2y)-3x^2y^2)

\int (cos (2 y) - 3 x^{2} y^{2}) d x

cos (2 y) x - y^{2} x^{3} + C

Solution steps

\int cos (2 y) - 3 x^{2} y^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (2 y) d x - \int 3 y^{2} x^{2} d x

\int cos (2 y) d x = cos (2 y) x

\int 3 y^{2} x^{2} d x = y^{2} x^{3}

= cos (2 y) x - y^{2} x^{3}

Add a constant to the solution

= cos (2 y) x - y^{2} x^{3} + C

\frac{d}{d x} (\frac{1}{2 3 x - 1})

f (x) = 8 (x - \frac{1}{x})^{4}, at x = 2

(sin (x^{'}))^{^{'}}

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

\int_{0}^{1} π (y - y^{2}) d y

What is the integral of (cos(2y)-3x^2y^2) ?
The integral of (cos(2y)-3x^2y^2) is cos(2y)x-y^2x^3+C