Lf -0-x2dx-x2-a2x2-b2x2-c2- -2a-bb-cc-a then -0-dx-x2-4x2-9-

The correct option is C π/60 ∫_0^∞ #10;x^2dx(x^2+a^2)(x^2+b^2)(x^2+c^2)=π2(a+b)(b+c)(c+a) #10; ∫_0^∞ #10;x^2dx(x^2+2^2)(x^2+3^2)(x^2+0)=π2 ...

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Method of Difference

lf ∫0∞x2dx/...

Question

lf $\int_{0}^{\infty} \frac{x^{2} d x}{(x^{2} + a^{2}) (x^{2} + b^{2}) (x^{2} + c^{2})} =$ $\frac{π}{2 (a + b) (b + c) (c + a)}$ then $\int_{0}^{\infty} \frac{d x}{(x^{2} + 4) (x^{2} + 9)} =$

\frac{π}{60}

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\frac{π}{20}

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\frac{π}{40}

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\frac{π}{80}

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Solution

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\int_{0}^{\infty} \frac{x^{2} d x}{(x^{2} + a^{2}) (x^{2} + b^{2}) (x^{2} + c^{2})} = \frac{π}{2 (a + b) (b + c) (c + a)}

\int_{0}^{\infty} \frac{1}{(x^{2} + 4) (x^{2} + 9)} d x

\infty \int 0 \frac{x^{2}}{(x^{2} + a^{2}) (x^{2} + b^{2}) (x^{2} + c^{2})} d x = \frac{π}{2 (a + b) (b + c) (c + a)}

\infty \int 0 \frac{d x}{(x^{2} + 4) (x^{2} + 9)}

If \infty \int 0 \frac{x^{2}}{(x^{2} + a^{2}) (x^{2} + b^{2}) (x^{2} + c^{2})} d x = \frac{π}{2 (a + b) (b + c) (c + a)} then, \infty \int 0 \frac{d x}{(x^{2} + 1) (x^{2} + 16)} =

f (x) = {sin}^{- 1} (\frac{x^{2} + 1}{x^{2} + 2})

\int_{0}^{\infty} e^{- x^{2}} d x = \frac{\sqrt{π}}{2}

\int_{0}^{\infty} e^{- a x^{2}} d x, a > 0

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