Mathematics

$$\int \dfrac { e ^ { x } } { x } \left( x \cdot ( \log x ) ^ { 2 } + 2 \log x \right) d x$$


SOLUTION
$$\int { \cfrac { { e }^{ x } }{ x } \left( x{ \left( \log { x }  \right)  }^{ 2 }+2\log { x }  \right)  } dx\\ =\int { \cfrac { { e }^{ x } }{ x } \left( x{ \left( \log { x }  \right)  }^{ 2 }+\cfrac { 2\log { x }  }{ x }  \right)  } dx\\ =\int { \cfrac { { e }^{ x } }{ x } \left( x{ \left( \log { x }  \right)  }^{ 2 } \right)  } +\int { \cfrac { { e }^{ x } }{ x }  } \cfrac { 2\log { x }  }{ x } dx\\ ={ e }^{ x }{ \left( \log { x }  \right)  }^{ 2 }-\int { { e }^{ x } } \cfrac { 2\log { x }  }{ x } dx+\int { { e }^{ x } } \cfrac { 2\log { x }  }{ x } dx+C\\ ={ e }^{ x }{ \left( \log { x }  \right)  }^{ 2 }+C$$
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Subjective Medium Published on 17th 09, 2020
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