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henriquerb

  • 3 years ago

Integrate sqrt(x)lnxdx

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  1. abb0t
    • 3 years ago
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    \[\int\limits \sqrt{x}\ln(x)dx\] I'm going to assume that's the correct integral, above. You're going to use parts, which takes the form: \[\int\limits udv = uv - \int\limits vdu\] u = ln(x) dv = √x \[du = \frac{ 1 }{ x }\] \[v = \frac{ 2 }{ 3 } x^{\frac{ 3 }{ 2 }}\]

  2. abb0t
    • 3 years ago
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    \[\frac{ 2 }{ 9 }x^{\frac{ 3 }{ 2 }}(3\ln(x)-2)+C\]

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