What is the integral of sqrt(t)sin(t) ?

The integral of sqrt(t)sin(t) is -sqrt(t)cos(t)+sqrt(pi/2)\C(sqrt(2/pi)sqrt(t))+C

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integral of sqrt(t)sin(t)

\int t sin (t) d t

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

Solution steps

\int t sin (t) d t

Apply Integration By Parts

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

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

= - t cos (t) - (- \frac{π}{2} C (\frac{2}{π} t))

Simplify

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

Add a constant to the solution

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

What is the integral of sqrt(t)sin(t) ?
The integral of sqrt(t)sin(t) is -sqrt(t)cos(t)+sqrt(pi/2)\C(sqrt(2/pi)sqrt(t))+C