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

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

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

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

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

Solution steps

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

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

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

= \frac{sin ^{2} ( x )}{2} - \frac{y ^{2} x ^{2}}{2}

Add a constant to the solution

= \frac{sin ^{2} ( x )}{2} - \frac{y ^{2} x ^{2}}{2} + C

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