What is the integral of (x^2)/2 y+x/2 y^2cos(z) ?

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

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integral of (x^2)/2 y+x/2 y^2cos(z)

\int \frac{x ^{2}}{2} y + \frac{x}{2} y^{2} cos (z) d z

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

Solution steps

\int \frac{x ^{2}}{2} y + \frac{x}{2} y^{2} cos (z) d z

Apply the Sum Rule:

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

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

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

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

= \frac{x ^{2}}{2} yz + \frac{x y ^{2}}{2} sin (z)

Add a constant to the solution

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

\frac{\partial}{\partial u} (e^{u})

\int_{2}^{3} \frac{x}{x ^{2} + 4 x + 20} d x

\frac{\partial}{\partial x} (\frac{x ^{2}}{x + y})

x \cdot ln (x)

\int \frac{x ^{2} - x - 1}{x ^{2} ( x - 1 )} d x

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