Fundamental Theorem of Calculus

The value of ${\int }_a^b\frac{\left|x\right|}{x}dx (a<b)$ is 

$\frac{1}{k}{\int }_{ak}^{bk}f\left(\frac{x}{k}\right)dx=$

${\int }_0^{\frac{\pi }{2}}\cos x{e}^{\sin x}dx=$

${\int }_0^{\frac{\pi }{2}}x\sin xdx=$

${\int }_0^{\pi }\frac{dx}{1+\sin x}=$

${\int }_1^{2}x{e}^{x}dx=$

${\int }_0^1\frac{x^3}{1+x^4}dx=$

${\int }_0^1\frac{dx}{e^x+e^{-x}}=$

${\int }_0^2\frac{dx}{\sqrt{4-x^2}}=$

${\int }_1^{\sqrt{3}}\frac{dx}{1+x^2}=$

${\int }_0^2\frac{dx}{x^2+4}=$

${\int }_2^3\frac{dx}{2x+1}=$

The value of $\underset{-1}{\overset{0}{\int }}\frac{dx}{x^2+2x+2}$ is equal to

The value of ${\int }_0^1{\mathrm{x}}^{10}\mathrm{dx}$ is _____. (Express your answer as a fraction)

If $\underset{0}{\overset{a}{\int }}\frac{1}{1+4x^2}dx=\frac{\pi }{8}$, then $a=$_____.

$\underset{0}{\overset{\frac{\pi }{2}}{\int }}\cos x{e}^{\sin x}dx$ is equal to _____.