Mathematics

# Solve:$\displaystyle \int\dfrac{1}{\sqrt{1+4x^2}}dx$

##### SOLUTION
$\int { \dfrac { 1 }{ \sqrt { 1+4{ { x }^{ 2 } } } } dx } \\ =\int { \dfrac { 1 }{ \sqrt { 4\left( \dfrac { 1+4{ x }^{ 2 } }{ 4 } \right) } } dx } \\ =\int { \left[ \dfrac { 1 }{ 2 } .\dfrac { 1 }{ \sqrt { \dfrac { 1 }{ 4 } +{ x }^{ 2 } } } \right] dx } \\ =\dfrac { 1 }{ 2 } \int { \dfrac { 1 }{ \sqrt { { \left( \dfrac { 1 }{ 2 } \right) }^{ 2 }+{ x }^{ 2 } } } dx } \\ =\dfrac { 1 }{ 2 } \left[ \dfrac { 1 }{ \dfrac { 1 }{ 2 } } { \tan }^{ -1 }\left( \dfrac { x }{ \dfrac { 1 }{ 2 } } \right) \right] +C\\ ={ \tan }^{ -1 }2x+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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Q2 Single Correct Medium
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