$\int x\sqrt{x-1}dx$ bằng:

A.  ${\left(\mathrm{x}-1\right)}^{\frac{5}{2}}+{\left(x-1\right)}^{\frac{3}{2}}+C$

B. $\frac{2}{15}\left[3{\left(\mathrm{x}-1\right)}^{\frac{5}{2}}-5{\left(x-1\right)}^{\frac{3}{2}}\right]+C$

C. $\frac{2}{15}\left[3{\left(\mathrm{x}-1\right)}^{\frac{5}{2}}+5{\left(x-1\right)}^{\frac{3}{2}}\right]+C$

D. $\frac{1}{15}\left[3{\left(\mathrm{x}-1\right)}^{\frac{5}{2}}+5{\left(x-1\right)}^{\frac{3}{2}}\right]+C$

Chứng minh rằng với số tự nhiên n > 2 thì  $A=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}$�=112+122+132+142+...+1�2không là số tự nhiên

Tính nhanh:

a) ${35}^2 – {15}^2$;                             b)  ${48}^2 - {42}^2 +64 - {52}^2$

c) ${72}^2 + 144.16+{16}^2 -{12}^2$      d)  $\frac{{43}^2-{11}^2}{{(36,5)}^2-{(27,5)}^2}$