Mathematics

Evaluate:$\displaystyle\int\dfrac{2x+3}{\sqrt{4x+3}}dx=$

SOLUTION
$\int { \dfrac { 2x+3 }{ \sqrt { 4x+3 } } } dx$
$\Rightarrow \dfrac { 1 }{ 2 } \int { \dfrac { \left( 4x+3 \right) }{ \sqrt { 4x+3 } } } +\dfrac { 3 }{ 2 } \int { \dfrac { dx }{ \sqrt { 4x+3 } } }$
$\Rightarrow 4x+3=m$
$dx=\dfrac { dm }{ 4 }$
$\Rightarrow \dfrac { 1 }{ 8 } \int { \dfrac { m }{ \sqrt { m } } dm } +\dfrac { 3 }{ 8 } \int { \dfrac { dm }{ \sqrt { m } } }$
$\Rightarrow \dfrac { 1 }{ 8 } \int { \sqrt { m } } dm+\dfrac { 3 }{ 8 } \int { { \left( \sqrt { m } \right) }^{ -1 } } dm$
$\Rightarrow \dfrac { 1 }{ 8 } \times \dfrac { 2 }{ 3 } \times { m }^{ 3/2 }+\dfrac { 3 }{ 8 } \times 2\times \sqrt { m } +c$
$\Rightarrow \dfrac { 1 }{ 12 } { \left( 4x+3 \right) }^{ 3/2 }+\dfrac { 3 }{ 4 } \sqrt { 4x+3 } +c$

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Subjective Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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