Question

x logx dx find the integration of x logx

Answer 1

Answer :

Now,

$\int x \: logx \: dx \\ \\ = logx \: \int x \: dx - \int ( \frac{d}{dx} (logx) \times \int x \: dx)dx \\ \\ = (logx) (\frac{ {x}^{2} }{2} ) - \int ( \frac{1}{x} \times \frac{ {x}^{2} }{2} )dx + c \\ \\ where \: \: c \: \: is \: \: integral \: \: constant \\ \\ = \frac{1}{2} {x}^{2} logx - \frac{1}{2} \int x \: dx + c \\ \\ = \frac{1}{2} {x}^{2} logx - \frac{1}{2} ( \frac{1}{2} {x}^{2} ) + c \\ \\ = \frac{1}{2} {x}^{2} (logx - \frac{1}{2} ) + c$

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