Let $g(x)=\displaystyle \int _{1-x}^{1+x}t|f'(t)|dt$, where $f(x)$ does not behave like a constant function in any interval $(a,b)$ and the graph of $y=f'(x)$ is symmetric about the line $x=1$, then

$\lim _{x \rightarrow 0} \int_{0}^{x} \frac{\left(\tan ^{-1} t\right)^{2}}{\sqrt{1+x^{2}}} d t$  is equal to-

যদি $\int Q \left ( x \right ) dx = \ln{\left ( \ln{x} \right )} + c$ হয়,  যেখানে c একটি ধ্রুবক, তবে Q(x)=?

  $\frac{d^{2} y}{dx^{2}} = \left ( \frac{1}{x^{2}} \right )$ হলে y এর মান নিচের কোনটি ?  

Let $f:(0, \infty) \rightarrow R$ and $\int^{2x}_0 (1+t)f(t) dt =-2x^3-\dfrac{x^2}{2} +2x+K$, where K is constant , then $\Sigma^8_{r=1} f(r)$ is equal to