115 4x 2x^2=0⇒ 15 4x 2x^2=0 ⇒ 2x^2+4x 15=0 x= 4±√(16 4× 2x 15)4= 4±√(16+120)4 x= 4±√(136)4= 4±2√(34)4 ...

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Integration of Irrational Algebraic Fractions - 2

Evaluate 11...

Question

Evaluate $\frac{1}{15 - 4 x - 2 x^{2}}$

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Solution

$\frac{1}{15 - 4 x - 2 x^{2}} = 0 \Rightarrow 15 - 4 x - 2 x^{2} = 0$
$\Rightarrow 2 x^{2} + 4 x - 15 = 0 x = \frac{- 4 \pm \sqrt{16 - 4 \times 2 x - 15}}{4} = \frac{- 4 \pm \sqrt{16 + 120}}{4} x = \frac{- 4 \pm \sqrt{136}}{4} = \frac{- 4 \pm 2 \sqrt{34}}{4}$

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