31]\int \frac{1}{x-1+\sqrt{x+1}} dx
32}[\int \frac{sinx}{\ln (2+x^{2}) }
33]\int_0^{\pi/3} \frac{sin^{n}x}{sin^{n}x+cos^{n}x} dx
34]\int {\frac{{1 - \sqrt x }}{{1 + \sqrt x }}dx}
35]\int {\frac{{dx}}{{x(1 + 2\sqrt x + \sqrt[3]{x})}}}
36]For t>0, find the minimum value of \int_{0}^{1}x|e^{-x^{2}}-t| dx.
37]Prove the following inequality for x≥0
\int_{0}^{x}(t-t^{2})\sin^{2004}t\ dt <\frac{1}{2006}
38]Let f(x) be the function defined for x≥0 which satisfies the following conditions.
a)f(x)=\begin{cases}x \ \ \ \ \ \ \ \ ( 0\leq x<1) \\ 2-x \ \ \ (1\leq x <2) \end{cases}
b) f(x+2n)= f(x) (n=0,1,2,3,...................)
find \lim_{n\to\infty}\int_{0}^{2n}f(x)e^{-x}\ dx.
39]\displaystyle\lim_{n\to\infty}\displaystyle\sum_{i = 1}^{n}\frac {1}{n}\cos \left(\frac {\pi i}{2n}\right)39]
40]\displaystyle\lim_{n\to\infty}\displaystyle\sum_{i = 1}^{n}\frac {3}{n}\sin \left(2\pi + \frac {3\pi i}{n}\right)