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

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

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integral of sqrt(y)sin(y)

\int y sin (y) d y

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

Solution steps

\int y sin (y) d y

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (x^{2} - 9)

\int arctan (\frac{2}{x}) d x

1 - u

y^{^{'}} = 4 - 0.75 y

n = 2 \sum \infty \frac{8}{n ^{2} - 1}

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