integral of sqrt(x)cos(x)

解答

\int x cos (x) d x

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

求解步骤

\int x cos (x) d x

使用分布积分法

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

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

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

解答补常数

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

t an g e n t \frac{8 x}{x ^{2} + 1}, at x = 0

\int_{0}^{3} (x 14 - x^{2}) d x

\frac{\partial}{\partial θ} (ρ sin (φ) sin (θ))

\int \frac{e ^{2 x}}{e ^{x} + 5} d x

\frac{\partial}{\partial x} (y (- 3 - x))