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
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