Evaluate ∫$$3x2tan$$⁡$$1x$$−$$xsec2$$⁡$$1xdx$$

Correct option is 1x3tan⁡1x+c

Questions

$Evaluate \int (3 x^{2} \tan \frac{1}{x} - x \sec^{2} \frac{1}{x}) d x$

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x3tan⁡1x+c

x2tan⁡1x+c

6xtan⁡1x+c

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detailed solution

Correct option is A

=∫3x2tan⁡1x−xsec2⁡1xdx=∫3x2tan⁡1xdx−∫xsec2⁡1xdx (apply integration by parts only for 1st integrand)=tan⁡1xx3−∫sec2⁡1x−1x2x3dx−∫xsec2⁡1xdx=x3tan⁡1x+c

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Evaluate ∫3x2tan⁡1x−xsec2⁡1xdx

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$Evaluate \int (3 x^{2} \tan \frac{1}{x} - x \sec^{2} \frac{1}{x}) d x$