Mathematics

# Solve : $\int \sin^{2} (2x+1) dx$

##### SOLUTION
$\int { \sin ^{ 2 }{ \left( 2x+1 \right) } dx }$
$=\cfrac { 1 }{ 2 } 2\sin ^{ 2 }{ \left( 2x+1 \right) dx }$
$=\cfrac { 1 }{ 2 } \int { 1-\cos { 2\left( 2x+1 \right) dx } }$
$=\cfrac { 1 }{ 2 } \int { dx } -\cfrac { 1 }{ 2 } \int { \cos { \left( 4x+2 \right) } dx }$
$=\cfrac { x }{ 2 } -\cfrac { 1 }{ 8 } \int { \cos { \left( 4x+2 \right) } d\left( 4x \right) }$
$=\cfrac { x }{ 2 } -\cfrac { \sin { \left( 4x+2 \right) } }{ 8 } +c$
$=\cfrac { 4x-\sin { \left( 4x+2 \right) } }{ 8 } +c$

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Subjective Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

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