What is the integral of-x^2y^2sin(x)+2xy^2cos(x) ?

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

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integral of-x^2y^2sin(x)+2xy^2cos(x)

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

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

Solution steps

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

(- 10, 9), (- 2, - 5)

{\frac{10}{s ( s + 2 )}}

\frac{d}{d x} (7 (x^{3} - x)^{4})

\int (3 x^{4} - 5 x) d x

\frac{d}{d x} (6 x + 29 cos (\frac{3 x}{4}) + 5 x^{2} + 3)

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