integral of (15x^{-1}-4sinh(x))

解答

\int (15 x^{- 1} - 4 sinh (x)) d x

15 ln ∣ x ∣ - 4 cosh (x) + C

求解步骤

\int 15 x^{- 1} - 4 sinh (x) d x

15 x^{- 1} = \frac{15}{x}

= \int \frac{15}{x} - 4 sinh (x) d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{15}{x} d x - \int 4 sinh (x) d x

\int \frac{15}{x} d x = 15 ln ∣ x ∣

\int 4 sinh (x) d x = 4 cosh (x)

= 15 ln ∣ x ∣ - 4 cosh (x)

解答补常数

= 15 ln ∣ x ∣ - 4 cosh (x) + C

\frac{d}{d x} ((x^{6} + 1)^{\frac{5}{2}})

\int tan^{3} (x) sec^{4} (x) d x

l a pl a ce t r an s f or m t^{\frac{3}{2}} \cdot e^{- 2 t}

\frac{\partial}{\partial s} (\frac{t}{s})

\int_{0}^{1} \frac{x ^{3}}{x ^{2} + 1} d x