For the integral $\int_0^{+\infty}\frac{dx}{(x^2+p^2)(x^2+q^2)}$, which of the following statements are CORRECT? A: $\frac{1}{q^2-p^2}[\frac{1}{p}-\frac{1}{q}]\frac{\pi}{2},p>0 \ q>0;$ B: $\frac{1}{q^2-p^2}[\frac{1}{q}+\frac{1}{p}]\frac{\pi}{2}, -p>0 \ -q>0;$ C: $\frac{1}{q^2-p^2}[\frac{1}{p}-\frac{1}{q}]\frac{\pi}{2}, p>0 \ -q>0;$ D: $\frac{1}{p^2-q^2}[\frac{1}{q}+\frac{1}{p}]\frac{\pi}{2}, -p>0 \ q>0.$

已知三阶矩阵`A`的特征值为`-1,1,2`，`A^**`表示`A`的伴随阵，则矩阵` B=(3A^**)^{-1} ` 的特征值为（ ） A: `1,-1,2`； B: `\frac{1}{6},-\frac{1}{6},-\frac{1}{3}`； C: `-\frac{1}{6},\frac{1}{6},\frac{1}{3}`； D: `\frac{1}{2},-\frac{1}{2},-1`。

积分$\int_0^1 x \arctan xdx=$（）。 A: $\frac{\pi}{4}+\frac{1}{2}$ B: $\frac{\pi}{4}$ C: $\frac{\pi}{4}-\frac{1}{2}$ D: $\frac{1}{2}$

\(\int{\sin 3x\cos 4xdx}\)=( )。 A: \(\frac{1}{2}\sin x-\frac{1}{14}\cos 7x+C\) B: \(\frac{1}{2}\cos x-\frac{1}{14}\cos 7x+C\) C: \(\frac{1}{2}\cos x+\frac{1}{14}\sin 7x+C\) D: \(\frac{1}{2}\sin x+\frac{1}{14}\sin 7x+C\)

将函数\(f(x)=\sin^4 x\)展开成Fourier级数为 ____ . A: \(f(x) = \frac{3}{8}-\frac{1}{2}\cos 2x +\frac{1}{8}cos 4x\) B: \(f(x) = \frac{1}{4}-\frac{1}{2}\cos x +\frac{3}{8}cos 4x\) C: \(f(x) = \frac{1}{4}-\frac{1}{2}\sin 2x -\frac{3}{8}cos 4x\) D: \(f(x) = \frac{3}{8}-\frac{1}{2}\sin x -\frac{1}{8}cos 4x\)

设`\n`阶方阵`\A`满足`\|A| = 2`，则`\|A^TA| = ,|A^{ - 1}| = ,| A^ ** | = ,| (A^ ** )^ ** | = ,|(A^ ** )^{ - 1} + A| = ,| A^{ - 1}(A^ ** + A^{ - 1})A| = `分别等于（ ） A: \[4,\frac{1}{2},{2^{n - 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^n},\frac{{{3^n}}}{2}\] B: \[2,\frac{1}{2},{2^{n - 1}},{2^{{{(n + 1)}^2}}},2{(\frac{3}{2})^n},\frac{{{3^n}}}{2}\] C: \[4,\frac{1}{2},{2^{n + 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^{n - 1}},\frac{{{3^n}}}{2}\] D: \[2,\frac{1}{2},{2^{n - 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^{n - 1}},\frac{{{3^n}}}{2}\]

1．下列数列中，收敛但极限不为$1$的是 A: ${{(2+\frac{1}{n})}^{\frac{1}{n}}}$ B: ${{n}^{\frac{1}{n}}}$ C: $\frac{1}{{{n}^{2}}+1}+\frac{2}{{{n}^{2}}+2}+\cdots +\frac{n}{{{n}^{2}}+n}$ D: $\frac{{{(n!)}^{2}}}{{{n}^{n}}}$

设方阵`\A`满足`\A^2 - A - 2E = 0`，则`\A^{-1}=` （ ） A: \[\frac{1}{2}(A - E)\] B: \[\frac{1}{2}(A + E)\] C: \[\frac{1}{4}(A - E)\] D: \[\frac{1}{4}(A + E)\]

\(\int { { {\sin }^{2}}x { { \cos }^{5}}xdx}\)=( ) A: \(\frac{1}{3} { { \sin }^{3}}x-\frac{2}{5} { { \sin }^{5}}x+\frac{1}{7} { { \sin }^{7}}x+C\) B: \(\frac{2}{3} { { \sin }^{3}}x-\frac{1}{5} { { \sin }^{5}}x-\frac{1}{7} { { \sin }^{7}}x+C\) C: \(\frac{1}{3} { { \cos }^{3}}x-\frac{2}{5} { { \cos }^{5}}x+\frac{1}{7} { { \cos }^{7}}x+C\) D: \(\frac{2}{3} { { \cos }^{3}}x-\frac{1}{5} { { \cos }^{5}}x-\frac{1}{7} { { \cos }^{7}}x+C\)

已知函数$y= \ln (1+ x) $，则$y''(x) =$( )。 A: $\frac{1}{(1+x)^2}$ B: $-\frac{1}{(1+x)^2}$ C: $-\frac{1}{1+x}$ D: $\frac{1}{1+x}$