What is the integral of ((ln(53))/v-ln(6)v^e) ?

The integral of ((ln(53))/v-ln(6)v^e) is ln(53)ln|v|-1/(e+1)ln(6)v^{e+1}+C

Popular >

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

\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

Solution steps

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

Apply the Sum Rule:

\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}

Add a constant to the solution

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

\int \frac{arcsin ( x )}{3 x ^{2}} d x

\int \frac{1}{t ^{2} + 2 t} d t

\int \frac{tan ( x ) + sec ( x )}{sec ^{2} ( x )} d x

\int sin (\frac{θ}{2}) tan (\frac{θ}{2}) d θ

\int (7 - csc (x) cot (x)) d x

What is the integral of ((ln(53))/v-ln(6)v^e) ?
The integral of ((ln(53))/v-ln(6)v^e) is ln(53)ln|v|-1/(e+1)ln(6)v^{e+1}+C