integral of ((-7)/x+e^{9x}+9/4)

解

\int (\frac{- 7}{x} + e^{9 x} + \frac{9}{4}) d x

- 7 ln ∣ x ∣ + \frac{1}{9} e^{9 x} + \frac{9}{4} x + C

解答ステップ

\int \frac{- 7}{x} + e^{9 x} + \frac{9}{4} d x

総和規則を適用する:

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

= \int \frac{- 7}{x} d x + \int e^{9 x} d x + \int \frac{9}{4} d x

\int \frac{- 7}{x} d x = - 7 ln ∣ x ∣

\int e^{9 x} d x = \frac{1}{9} e^{9 x}

\int \frac{9}{4} d x = \frac{9}{4} x

= - 7 ln ∣ x ∣ + \frac{1}{9} e^{9 x} + \frac{9}{4} x

定数を解答に追加する

= - 7 ln ∣ x ∣ + \frac{1}{9} e^{9 x} + \frac{9}{4} x + C