integral of (cos(sqrt(x)))/(sqrt(x))

解答

\int \frac{cos ( x )}{x} d x

2 sin (x) + C

求解步骤

\int \frac{cos ( x )}{x} d x

使用换元积分法

= \int 2 cos (u) d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int cos (u) d u

使用积分常见定则:

\int cos (u) d u = sin (u)

= 2 sin (u)

u = x

代回

= 2 sin (x)

解答补常数

= 2 sin (x) + C

\frac{\partial}{\partial x} (x z^{2})

\int \frac{5}{6 + 5 x} d x

\int \frac{1 - x ^{2}}{x ^{4}} d x

(x, y) \to (0, 0) lim (x y^{2})

\int \frac{1}{x 4 x ^{2} + 9} d x