Question

integrate dx/x^2-6x+11

Answer 1

Hey!

= ∫ dx / x² - 6x + 11

= ∫ dx / x² - 2. 3. x + 9 + 2
= ∫ dx / (x-3)^2 + (√2)^2

using the formula,
∫ dx / x² + a² = 1/a tan^-1 (x/a) + C

= 1/√2 tan^-1 ( x-3 / √2 ) + C

Hope it helps!

Answer 2

$\large{→}$ ${\large{\boxed{\sf{∫\frac{1}{x²-6x+11}.dx}}}}$

$\large{=}$ ${\large{\boxed{\sf{∫\frac{1}{x²-6x+9+2}.dx}}}}$

$\large{=}$ ${\large{\boxed{\sf{∫\frac{1}{(x-3)²+(\sqrt{2})²}.dx}}}}$

${\large{\boxed{\red{\sf{∫\frac{1}{x²+a²}.dx=\frac{1}{a}Tan^{-1} (\frac{x}{a})+c}}}}}$

$\large{=}$ ${\large{\boxed{\sf{\frac{1}{\sqrt{2}}Tan^{-1} (\frac{x-3}{\sqrt{2}})+c}}}}$