What is the integral of sin(t/2)t ?

The integral of sin(t/2)t is -2tcos(t/2)+4sin(t/2)+C

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integral of sin(t/2)t

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

- 2 t cos (\frac{t}{2}) + 4 sin (\frac{t}{2}) + C

Solution steps

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

Apply Integration By Parts

: - 2 t cos (\frac{t}{2}) - \int - 2 cos (\frac{t}{2}) d t

= - 2 t cos (\frac{t}{2}) - \int - 2 cos (\frac{t}{2}) d t

\int - 2 cos (\frac{t}{2}) d t = - 4 sin (\frac{t}{2})

= - 2 t cos (\frac{t}{2}) - (- 4 sin (\frac{t}{2}))

Simplify

= - 2 t cos (\frac{t}{2}) + 4 sin (\frac{t}{2})

Add a constant to the solution

= - 2 t cos (\frac{t}{2}) + 4 sin (\frac{t}{2}) + C

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What is the integral of sin(t/2)t ?
The integral of sin(t/2)t is -2tcos(t/2)+4sin(t/2)+C