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

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

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integral of-x^2sin(y)

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

x^{2} cos (y) + C

Solution steps

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

Use the common integral:

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

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

Simplify

= x^{2} cos (y)

Add a constant to the solution

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

\frac{d}{d x} ((arccot (x))^{5})

\int \frac{- 1}{y ^{2} + 1} d y

y^{^{''}} + 2 y = sin (2 t), y (0) = 0, y^{^{'}} (0) = 0

\int \frac{1}{sec ( x ) + tan ( x )} d x

\frac{1}{s ^{3} + 8 s ^{2} + 12 s}