Mathematics

# Integrate:$\int \frac{1-V}{1+V^{2}}dv.$

##### SOLUTION
$\int \frac{1-v}{1+v^{2}}dv$
let $v = tan\theta$ ___(1)
$dv = sec^{2}\theta d\theta$
$\int \frac{1-tan\theta }{1+tan^{2}\theta }\times sec^{2}\theta d\theta$
$\int \frac{1-tan\theta }{sec^{2}\theta }\times sec^{2}\theta d\theta$
$\int d\theta -\int tan\theta d\theta$
$\theta -(-ln(cos\theta ))+c$  $[\because \int tan\theta d\theta = ln\, tan\theta ]$
$\theta +ln(cos\theta )+c$___(2)
from (1)
$\theta = tan^{-1}v$
putting in (1)
$tan^{-1}v+ln(tan^{-1}v)+c$ Ans

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

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