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$\int \frac{dx}{9 x^{2} + 6 x + 5}$ is equal to

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tan−1⁡3x+12+C

6tan−1⁡3x+12+C

cot−1⁡3x+12+C

16tan−1⁡3x+12+C

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detailed solution

Correct option is D

∫dx9x2+6x+5=19∫dxx2+23x+59 =19∫dxx2+2⋅13⋅x+132+59−132=19∫dxx2+23x+132+59−19=19∫dxx+132+232=1912/3tan−1⁡x+132/3+C ∵∫dxa2+x2=1atan−1⁡xa =16tan−1⁡3x+12+C

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∫dx9x2+6x+5is equal to

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$\int \frac{dx}{9 x^{2} + 6 x + 5}$ is equal to