integral of (cos(x^2))/x

解答

\int \frac{cos ( x ^{2} )}{x} d x

\frac{1}{2} Ci (x^{2}) + C

求解步骤

\int \frac{cos ( x ^{2} )}{x} d x

使用换元积分法

= \int \frac{cos ( u )}{2 u} d u

提出常数:

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

= \frac{1}{2} \cdot \int \frac{cos ( u )}{u} d u

这是非初等函数积分:

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

= \frac{1}{2} Ci (u)

u = x^{2}

代回

= \frac{1}{2} Ci (x^{2})

解答补常数

= \frac{1}{2} Ci (x^{2}) + C

d er i v a t i v e (\frac{1}{2})^{x - 1} + 3

\int \frac{x ^{3}}{a ^{2} - x ^{2}} d x

d er i v a t i v e \frac{t ^{5} - 3 t ^{2}}{2 t}

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

d er i v a t i v e f (x) = 7 e^{- x} - 4 e^{- 7 x}