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

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

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integral of sin(r^2)r

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

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

Solution steps

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

Apply u-substitution

= \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

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