Mathematics

Solve:
$$\int\dfrac{x^{2}+1}{x^{2}-4x+6}dx$$                                                                          


SOLUTION
$$\begin{array}{l} \int _{  }^{  }{ \dfrac { { { x^{ 2 } }+1 } }{ { { x^{ 2 } }-4x+6 } } dx } \\\\=\int _{  }^{  }{ \left( { \dfrac { { 4x-5 } }{ { { x^{ 2 } }-4x+6 } } +1 } \right) dx }  \\\\ =\int _{  }^{  }{ \dfrac { { 4x-5 } }{ { { x^{ 2 } }-4x+6 } } dx } +\int _{  }^{  }{ 1dx }  \\ =2\ln { \left( { { x^{ 2 } }-4x+6 } \right)  } +x+\dfrac { { 3ta{ n^{ -1 } }\left( { \dfrac { { x-2 } }{ { \sqrt { 2 }  } }  } \right)  } }{ { \sqrt { 2 }  } } +C \end{array}$$
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Subjective Medium Published on 17th 09, 2020
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