If $$f(x)=log$$⁡$$xx3$$, then its antiderivative $$F(x)given$$ by

Correct option is 1C−12x2log⁡(xe)

Questions

If $f (x) = \frac{\log x}{x^{3}}$ , then its antiderivative $F (x)$
given by

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C−12x2log⁡(xe)

C+12x2log⁡x

C−12x2log⁡(xe)

C+12x3log⁡(xe)

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detailed solution

Correct option is A

F(x)=∫log⁡xx3dx=log⁡x∫1x3dx−∫1x∫1x3dxdx =−12x2log⁡x+12∫1x3dx+ Constant =−12x2log⁡x−14x2+C=−12x2log⁡x+12log⁡e+C=−12x2log⁡xe+C

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If f(x)=log⁡xx3, then its antiderivative F(x)given by

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free study material

If $f (x) = \frac{\log x}{x^{3}}$ , then its antiderivative $F (x)$
given by