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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $ \int \large\frac{7}{3} \bigg( \frac{1}{x}-\frac{1}{x^2 }\bigg)$$ \times a (\log x + \large\frac{1}{x} ) $$dx$

$(a)\;\frac{7}{3} \frac{a (\log x +1/x)}{\log _e a }+c \\(b)\; \frac{a (\log x +1/x)}{x+1/x}+c \\(c)\; \frac{(\log x +1/x)}{x^2}+c \\ (d)\;None$

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A)
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$\log x +\large\frac{1}{x}=t$
$\bigg(\large\frac{1}{x} -\frac{1}{x^2}\bigg)$$dx=dt$
=> $\large\frac{7}{3} $$\int a^t.dt$
=> $\large\frac{7}{3} \frac{a^t}{\log_e a}+c$
$\large\frac{7}{3} \frac{a (\log x +1/x)}{\log _e a }+c $
Hence a is the correct answer.
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