If ∫$$dxx5x2$$−$$3=Ktan$$−$$1$$⁡$$f(x)+C$$ then

Correct option is 2f(x)=53x2−1,K=13

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If $\int \frac{d x}{x \sqrt{5 x^{2} - 3}} = K \tan^{- 1} f (x) + C$ then

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f(x)=53x2−1,K=15

f(x)=53x2−1,K=13

f(x)=125x2−3,K=15

none of these

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detailed solution

Correct option is B

Putting 5x2−3=t2 so 5xdx=tdt∫dxx5x2−3=∫xdxx25x2−3=15∫5tdtt2+3t=∫dtt2+3=13tan−1⁡t3+C=13tan−1⁡5x2−33+C.

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If ∫dxx5x2−3=Ktan−1⁡f(x)+C then

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If $\int \frac{d x}{x \sqrt{5 x^{2} - 3}} = K \tan^{- 1} f (x) + C$ then