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

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

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integral of sin(x)sqrt(x)

\int sin (x) x d x

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

Solution steps

\int sin (x) 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

x y^{2} y^{^{'}} = 2 - y^{3}

y = x - 3, y^{2} = 2 x + 18

f (x) = \frac{1}{2 + 3 x}, at x = 2

\int \frac{13}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

\int ln ∣ x ∣ \cdot 3 x d x

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