What is the integral of xycos(z) ?

The integral of xycos(z) is xysin(z)+C

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integral of xycos(z)

\int x y cos (z) d z

x y sin (z) + C

Solution steps

\int x y cos (z) d z

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x y \cdot \int cos (z) d z

Use the common integral:

\int cos (z) d z = sin (z)

= x y sin (z)

Add a constant to the solution

= x y sin (z) + C

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

\frac{\partial}{\partial x} (- x y)

\int \frac{2 x}{( x ^{2} + 4 ) ln ( x ^{2} + 4 )} d x

\int \frac{t}{9 + t ^{4}} d t

\frac{d y}{d x} = (1 - x) y^{2}, y (0) = - \frac{1}{12}