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

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

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integral of z^2sin(x)

\int z^{2} sin (x) d x

- z^{2} cos (x) + C

Solution steps

\int z^{2} sin (x) d x

Take the constant out:

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

= z^{2} \cdot \int sin (x) d x

Use the common integral:

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

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

Simplify

= - z^{2} cos (x)

Add a constant to the solution

= - z^{2} cos (x) + C

y^{^{''''}} + y = 0

\frac{d y}{d x} = \frac{y ^{2}}{2 x + 3}

\int \frac{x ^{3}}{4 - x ^{4}} d x

\int \frac{sec ^{2} ( x )}{3 + tan ^{2} ( x )} d x

y^{^{''}} - 4 y^{^{'}} + 3 y = t, y (0) = 1, y^{^{'}} (0) = 0