What is the integral of rsin(r^2) ?

The integral of rsin(r^2) is -1/2 cos(r^2)+C

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integral of rsin(r^2)

\int r sin (r^{2}) d r

- \frac{1}{2} cos (r^{2}) + C

Solution steps

\int r sin (r^{2}) d r

Apply u-substitution

: \int \frac{sin ( u )}{2} d u

= \int \frac{sin ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{2} (- cos (u))

Substitute back

u = r^{2}

= \frac{1}{2} (- cos (r^{2}))

Simplify

= - \frac{1}{2} cos (r^{2})

Add a constant to the solution

= - \frac{1}{2} cos (r^{2}) + C

\frac{d y}{d t} = y + 2 e^{t}

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

\int \frac{2 x ^{2} + 6}{( x ^{2} - 2 x + 2 ) ^{2}} d x

x \to \infty lim (ln (2 x))

x = - 1, x = 3, y = x^{3} - 1, y = 0

What is the integral of rsin(r^2) ?
The integral of rsin(r^2) is -1/2 cos(r^2)+C