If {d}\frac{dx}{f}(x) = 2x + \frac{3}{x} and f(1) = 1, then ...

CBSE Class 12 Math 2023 All Sets Solved Paper

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\;{d}{dx}/{f}(x) = 2x + \;{3}/{x}

and f(1) = 1, then f(x) is

Solution:

Given equation is

\;{d}{dx}/{f}(x) = 2x + \;{3}/{x}

Integrating on both sides

∫\;{d}{dx}/{f}(x)dx = ∫(2x + \;{3}/{x})dx

⇒ f(x) = x^2 + 3ln | x | + c...(i)

Given that f(1) = 1

∴ f(1) = 1 = 1 + c⇒ c = 0

∴ f(x) = x^2 + 3ln | x |

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