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

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

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integral of sqrt(y)cos(y)

\int y cos (y) d y

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

Solution steps

\int y cos (y) d y

Apply Integration By Parts

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

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

\int \frac{sin ( y )}{2 y} d y = \frac{π}{2} § (\frac{2}{π} y)

= y sin (y) - \frac{π}{2} § (\frac{2}{π} y)

Add a constant to the solution

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

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\int (5 + x^{7})^{8} 7 x^{6} d x

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