Question

integration of dx/ 4x²-4x+3​

Answer 1

$\huge\mathfrak\green{\bold{\underline{☘{ ℘ɧεŋσɱεŋศɭ}☘}}}$

$\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}$integration of dx/ 4x²-4x+3

$\huge\tt{\boxed{\overbrace{\underbrace{\blue{Answer</p><p> }}}}}$

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$\huge\tt⟹ ∫ \frac{dx}{4 {x}^{2} - 4x + 3}$

$\huge\tt⟹\frac{1}{4} ∫ \frac{dx}{ {x}^{2} - 4x + 3}$

By completing the square method :-

$\huge\tt⟹\frac{1}{4} ∫ \frac{dx}{ {(x - 2)}^{2} + 3 - {(2)}^{2} }$

$\huge\tt⟹ \frac{1}{4} ∫ \frac{dx}{ {(x - 2)}^{2} + 3 - 4 }$

$\huge\tt⟹ \frac{1}{4} ∫ \frac{dx}{ {(x - 2)}^{2} - {(1)}^{2} }$

Here ,this identity is used :-

$\huge\tt\frac{1}{2a} log | \frac{x - a}{x + a} | + c$

$\huge\tt= \frac{1}{2} log | \frac{x - 2 - 1}{x - 2 + 1} | + c$

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