integral of sqrt(cos(2x))

解答

\int cos (2 x) d x

E (2∣ \frac{2 x}{2}) + C

求解步骤

\int cos (2 x) d x

使用换元积分法

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

这是非初等函数积分:

\int cos (x) d x = 2 E (\frac{x}{2} ∣ 2)

= \frac{1}{2} \cdot 2 E (\frac{u}{2} ∣ 2)

u = 2 x

代回

= \frac{1}{2} \cdot 2 E (\frac{2 x}{2} ∣ 2)

化简

\frac{1}{2} \cdot 2 E (\frac{2 x}{2} ∣ 2) : E (2∣ \frac{2 x}{2})

= E (2∣ \frac{2 x}{2})

解答补常数

= E (2∣ \frac{2 x}{2}) + C

\frac{d P}{d t} = - \frac{1}{2} P + t

\frac{d y}{d x} = x^{2} sec (y)

\frac{d}{d x} (3 x \cdot e^{2 x})

x \to \infty lim (\frac{e ^{\frac{1}{x}}}{arctan ( x )})

\int 7 x sin (x) d x