integral of ((ln(53))/v-ln(6)v^e)

解答

\int (\frac{ln ( 53 )}{v} - ln (6) v^{e}) d v

ln (53) ln ∣ v ∣ - \frac{1}{e + 1} ln (6) v^{e + 1} + C

求解步骤

\int \frac{ln ( 53 )}{v} - ln (6) v^{e} d v

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{ln ( 53 )}{v} d v - \int ln (6) v^{e} d v

\int \frac{ln ( 53 )}{v} d v = ln (53) ln ∣ v ∣

\int ln (6) v^{e} d v = \frac{1}{e + 1} ln (6) v^{e + 1}

= ln (53) ln ∣ v ∣ - \frac{1}{e + 1} ln (6) v^{e + 1}

解答补常数

= ln (53) ln ∣ v ∣ - \frac{1}{e + 1} ln (6) v^{e + 1} + C

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