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

= \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

\frac{2}{5 x ^{4}}

x \to 2 lim (\frac{4 - 2 x}{x - 2})

c e^{x}

3 y d y = (2 sin (2 x) - e^{x}) y d x

\frac{\partial}{\partial x} (3 x^{6} y^{2})

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