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

Integrate : $\int x.2^x dx$

$(a)\;\frac{x.2^x}{\log_e 2}- \frac{1}{[\log 2]}\times \frac{2^x}{[\log 2]}+c \\(b)\;x.2^x-2^x+c \\(c)\;x-2^{x+c} \\ (d)\;None$

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A)
=> $\large\frac{x.e^x}{\log _e 2}- \int \frac{1.2^x }{\log _e 2}$$dx$
=> $ \large\frac{x.2^x}{\log _e 2} -\frac{1}{[\log 2]} \times \large\frac{2^x}{[\log ^2 ]}$$+c$
$\large\frac{x.2^x}{\log_e 2}- \frac{1}{[\log 2]}\times \frac{2^x}{[\log 2]}+c $
Hence a is the correct answer.
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