Question:

Given that $\int_{0}^{\infty}\frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)\left(x^{2}+c^{2}\right)}$ dx = $\frac{\pi}{2\left(a+b\right)\left(b+c\right)\left(c+a\right)'}$ then $\int_{0}^{\infty}\frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)}$ is

Updated On: Jun 14, 2022

$\frac{\pi}{60}$
$\frac{\pi}{20}$
$\frac{\pi}{40}$
$\frac{\pi}{80}$

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The Correct Option is A

Solution and Explanation

Answer (a)

\frac{\pi}{60}

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Concepts Used:

Integrals of Some Particular Functions

There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.

Integrals of Some Particular Functions:

∫1/(x² – a²) dx = (1/2a) log|(x – a)/(x + a)| + C
∫1/(a² – x²) dx = (1/2a) log|(a + x)/(a – x)| + C
∫1/(x² + a²) dx = (1/a) tan-1(x/a) + C
∫1/√(x² – a²) dx = log|x + √(x² – a²)| + C
∫1/√(a² – x²) dx = sin-1(x/a) + C
∫1/√(x² + a²) dx = log|x + √(x² + a²)| + C

These are tabulated below along with the meaning of each part.