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If $\int_{0}^{\infty} \frac{d x}{(x^{2} + 4) (x^{2} + 9)} = k π$ then the value of $k$ is

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Correct option is A

∫0∞ dxx2+4x2+9=15∫0∞ 1x2+4−1x2+9dx=1512tan−1⁡ x2−13tan−1⁡ x30∞=15π4−π6=π60, so k=160.

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If ∫0∞ dxx2+4x2+9=kπ then the value of k is

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If $\int_{0}^{\infty} \frac{d x}{(x^{2} + 4) (x^{2} + 9)} = k π$ then the value of $k$ is