integral of sin(x)sqrt(x)

解答

\int sin (x) x d x

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

求解步骤

\int sin (x) x d x

使用分布积分法

= - 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))

化简

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

解答补常数

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