Mathematics

# $\int \dfrac { \sin 2 x } { 1 + \sin ^ { 2 } x }$

##### SOLUTION
$\int { \dfrac { \sin2x }{ 1+{ \sin }^{ 2 }x } } dx$
$=\int { \dfrac { 2sinxcosx }{ 1+{ \sin }^{ 2 }x } } dx$
Take $u=1+{ \sin }^{ 2 }x$
$du=2sinxcosxdx$
$\therefore$   $\int { \dfrac { 1 }{ u } } du=log\left( 1+{ \sin }^{ 2 }x \right) +C$

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

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