What is the integral of (tsin(t^2)) ?

The integral of (tsin(t^2)) is -1/2 cos(t^2)+C

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integral of (tsin(t^2))

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

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

Solution steps

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

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 = t^{2}

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

Simplify

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

Add a constant to the solution

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

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