MCQ
$\int\left(e^{e x \log _e x}+\frac{\log _e x}{e^{-e x \log _e x}}\right) d x=\ldots \ldots \ldots+c$
- A$\frac{x^{-e x}}{e}$
- ✓$\frac{x^{e x}}{e}$
- C$-\frac{x^{e x}}{e}$
- D$\log (x-e)$
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$\left[\frac{x}{\sqrt{x^{2}-y^{2}}}+e^{\frac{y}{x}}\right] x \frac{d y}{d x}=x+\left[\frac{x}{\sqrt{x^{2}-y^{2}}}+e^{\frac{y}{x}}\right] y$ નો ઉકેલ
વક્ર $y=y(x)$ એે બિંદુઓ $(1,0)$ અને $(2 \alpha, \alpha)$ માંથી પસાર થાય, તો $\alpha>0$ નુ............ મૂલ્ય છે