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 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

= - 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

\int \frac{1}{3 x ^{2} + 6 x + 78} d x

\int e^{4 x} cos (7 x) d x

\frac{\partial}{\partial x} (\frac{2}{x z - z ^{4} + x ^{2}})

t^{2} \frac{d y}{d t} + y = 0, y (6) = - 3, t > 0

x \to 3 + lim (3 ln (x - 2))

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