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
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