Question

integration v/1-v dv

Answer 1

Answer:

Find the attachement

Step-by-step explanation:

Hope this helps you

Answer 2

Concept

The formula will we use

1. $\int \frac{1}{x}dx=\log x$

2. $\int x^ndx=\frac{x^{n+1}}{n+1}$

Given

The expression  $\frac{v}{1-v}$.

Find

We have to find the integration of the given expression.

Solution

Integrate the given function with respect to x.

$\begin{aligned}\int \frac{v}{1-v} d v &=-\int \frac{-v}{1-v} d v\\&=-\int \frac{1-v-1}{1-v} d v \\&=-\left\{\int \frac{1-v}{1-v} d v-\int \frac{1}{1-v} d v\right\} \\&=-\left\{\int d v-\int \frac{1}{1-v} d v\right\}\end{aligned}$

                 = -[v-{-log(1-v)}]

                 = -v -  log(1-v) +c

Hence the final value is -v -  log(1-v) +c.