Mathematics

Solve:$$\int x^2\sin 2xdx$$


SOLUTION
$$\int { { x }^{ 2 }\sin2xdx } \\ ={ x }^{ 2 }\int { \sin2xdx } -\int { \left[ \dfrac { d }{ dx } { x }^{ 2 }.\int { \sin2xdx }  \right]  } dx\\ =-\dfrac { { x }^{ 2 } }{ 2 } \cos2x+\int { x.\cos2xdx } \\ =-\dfrac { { x }^{ 2 } }{ 2 } \cos2x+\dfrac { x }{ 2 } \sin2x-\dfrac { \cos2x }{ 4 } +C\\ =\dfrac { 2x\sin2x-2{ x }^{ 2 }\cos2x-\cos2x }{ 4 } +C$$
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Subjective Medium Published on 17th 09, 2020
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