Question

निम्नलिखित प्रश्न को फलन का समाकलन कीजिए।

x log x

Answer 1

माना ${\displaystyle I=\int x\log x dx}$

${\displaystyle =\log x\int x dx-\int [\frac{d}{dx}\left(\log x\right)\int x dx]dx}$

${\displaystyle =\log x\left(\frac{x^2}{2}\right)-\int (\frac{1}{x}\cdot \frac{x^2}{2})dx}$

${\displaystyle =\frac{x^2}{2}\log x-\frac{1}{2}\int x dx+C}$

${\displaystyle =\frac{x^2}{2}\log x-\frac{1}{2}\times \frac{x^2}{2}+C}$

${\displaystyle =\frac{x^2}{2}\log x-\frac{1}{4}{x}^2+C}$