Mathematics

Evaluate:$$\int \frac{1}{x^{4}-1}dx$$


SOLUTION
$$\begin{array}{l} \int _{  }^{  }{ \dfrac { 1 }{ { { x^{ 4 } }-1 } } { dx } } =\int _{  }^{  }{ \dfrac { 1 }{ { \left( { x-1 } \right) \left( { x+1 } \right) \left( { { x^{ 2 } }+1 } \right)  } } { dx } }  \\ =\int _{  }^{  }{ \left( { -\dfrac { 1 }{ { 2\left( { { x^{ 2 } }+1 } \right)  } } -\dfrac { 1 }{ { 4\left( { x+1 } \right)  } } +\dfrac { 1 }{ { 4\left( { x-1 } \right)  } }  } \right)  } dx \\ =-\dfrac { { \ln { \left( { x+1 } \right)  }  } }{ 4 } -\dfrac { { { { \tan   }^{ -1 } }\left( x \right)  } }{ 2 } +\dfrac { { \ln { \left( { x-1 } \right)  }  } }{ 4 } +C \end{array}$$
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Subjective Medium Published on 17th 09, 2020
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