integral of (4^x-1/(3x))

解

\int (4^{x} - \frac{1}{3 x}) d x

\frac{2 ^{2 x - 1}}{ln ( 2 )} - \frac{1}{3} ln ∣ x ∣ + C

解答ステップ

\int 4^{x} - \frac{1}{3 x} 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 4^{x} d x - \int \frac{1}{3 x} d x

\int 4^{x} d x = \frac{2 ^{2 x - 1}}{ln ( 2 )}

\int \frac{1}{3 x} d x = \frac{1}{3} ln ∣ x ∣

= \frac{2 ^{2 x - 1}}{ln ( 2 )} - \frac{1}{3} ln ∣ x ∣

定数を解答に追加する

= \frac{2 ^{2 x - 1}}{ln ( 2 )} - \frac{1}{3} ln ∣ x ∣ + C