What is the integral of sqrt(x)*sin(x) ?

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

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integral of sqrt(x)*sin(x)

\int x \cdot sin (x) d x

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

Solution steps

\int x sin (x) d x

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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