integral of sinh(14x)

解答

\int sinh (14 x) d x

\frac{1}{14} cosh (14 x) + C

求解步骤

\int sinh (14 x) d x

使用换元积分法

= \int sinh (u) \frac{1}{14} d u

提出常数:

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

= \frac{1}{14} \cdot \int sinh (u) d u

使用积分常见定则:

\int sinh (u) d u = cosh (u)

= \frac{1}{14} cosh (u)

u = 14 x

代回

= \frac{1}{14} cosh (14 x)

解答补常数

= \frac{1}{14} cosh (14 x) + C

\int x^{- 1} sin (x) d x

x \to 0 lim (\frac{1 - cos ( 5 x )}{x})

\int sin (π x) sin (nπ x) d x

\frac{d}{d x} (x^{3} \cdot ln (x))

d er i v a t i v e y = y