Mathematics

# Integrate:$\int _{ 0 }^{ \pi }{ \dfrac { dx }{ 5+3cosx } }$

##### SOLUTION

$\int 1/5+3cosx. dx$

use$t=tanx/2$ thus, $cosx=1-t^2/1+t^2$ and $cos^(2)x/2=1/(1+t)^2$

$dt/dx=1/2.sec^(2).x/2$
$dt/dx=([1+t^2]/2)$

By substitution, we eliminate cosx etc and get ...
int $1/5+3cosx. dx = int 2/(8-2t^2). dt$
=int$1/(4-t^2).dt$
=$1/4.ln([2+t]/[2-t]) + C$

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

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