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$\int x^{x} (1 + \log | x |) dx$ is equal to

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xxlog ⁡|x|+C

exx+C

xx+C

None of these

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Correct option is C

putxx=t⇒xx1+loge ⁡|x|dx=dt∫xx1+loge∣x!dx=t+C=xx+C

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∫xx(1+log ⁡|x|)dx is equal to

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$\int x^{x} (1 + \log | x |) dx$ is equal to