MCQ
$\int\frac{(1+\text{log x})^2}{1+\text{x}^2}\text{dx}=$
- ✓$\frac{1}{3}(1+\text{log})^3+\text{c}$
- B$\frac{1}{2}(1+\text{log})^2+\text{c}$
- C$\log(\text{log }1+\text{x})+2$
- D$\text{None of these}$
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$\left[\frac{x}{\sqrt{x^{2}-y^{2}}}+e^{\frac{y}{x}}\right] x \frac{d y}{d x}=x+\left[\frac{x}{\sqrt{x^{2}-y^{2}}}+e^{\frac{y}{x}}\right] y$
pass through the points $(1,0)$ and $(2 \alpha, \alpha), \alpha>0$.
Then $\alpha$ is equal to
Statement $-2$ : The function $f(x) = x\, log\, x$ is an increasing function in $[1, 2]$ and $g (x) = 2 -x$ is a decreasing function in $[ 1 , 2]$ and the graphs represented by these functions intersect at a point in $[ 1 , 2]$