Math, asked by Anonymous, 9 months ago

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Answered by Amrit111Raj82
1

MARK AS BRAINLIEST...........

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Answered by Anonymous
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\displaystyle\int{  \dfrac{  { x  }^{ 2  }  -2  }{ ( { x  }^{ 4  }  +5 { x  }^{ 2  }  +4) \arctan (   \dfrac{  { x  }^{ 2  }  +2  }{ x  }     )    }    }d x

∫arctan(x2)4+x2dx

We can use substitution. Let u=arctan(x2). Taking the derivative, we see that du=121+(x2)2dx=124+x24dx=24+x2dx.Thus:=12∫2arctan(x2)4+x2dx=12∫udu=12(u22)=u24=14arctan2(x2)

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