Mathematics

# Evaluate: $\displaystyle\int \frac { 1 } { ( x + 2 ) \sqrt { x + 1 } } d x$

$2 \tan ^ { - 1 } ( \sqrt { x + 1 } ) + c$

##### SOLUTION
$I=\displaystyle\int _{ }^{ }{ \frac { 1 }{ { (x+2)\sqrt { x+1 } } } dx }$

$Substitute\, u=\sqrt { x+1 }$

$du=\dfrac 1{2\sqrt{x+1}}dx$

$=2\displaystyle\int _{ }^{ }{ \dfrac { 1 }{ { 1+{ u^{ 2 } } } } du }$

$=2{ \tan ^{ -1 } }u+C$

$=2{ \tan ^{ -1 } }\left( { \sqrt { x+1 } } \right) +C$

Hence the correct option is $A,\,2{ \tan ^{ -1 } }\left( { \sqrt { x+1 } } \right) +C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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