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

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

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integral of x^2cos(y)

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

x^{2} sin (y) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= x^{2} sin (y)

Add a constant to the solution

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

\int \frac{2}{y} d y

3 x^{5} x

\frac{d}{d t} (2 + 4 t)

8 x y \frac{d y}{d x} = 1

\int cos^{3} (\frac{x}{16}) d x