Mathematics

$$\int {\frac{{dx}}{{\sqrt {2 - 4x + {x^2}} }}} $$=?


SOLUTION
$$\begin{array}{l} \int { \frac { { dx } }{ { \sqrt { 2-4x+{ x^{ 2 } } }  } }  }  \\ =\int { \frac { { dx } }{ { \sqrt { { x^{ 2 } }-4x+4-2 }  } }  }  \\ =\int { \frac { { dx } }{ { \sqrt { { { \left( { x-2 } \right)  }^{ 2 } }-{ { \left( { \sqrt { 2 }  } \right)  }^{ 2 } } }  } }  }  \\ =\log  |\left( { x-2 } \right) +\sqrt { { { \left( { x-2 } \right)  }^{ 2 } }-2+C } |+C \\ =\log  |x-2+\sqrt { { x^{ 2 } }-4x+2 } |+C \end{array}$$
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Subjective Medium Published on 17th 09, 2020
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