a)Đặt $ t=ln
x\Rightarrow\int(\frac{1}{ln^2x}-\frac{1}{ln
x})dx=\int(\frac{1}{t^2}-\frac{1}{t})de^t$
$=\int(-e^td\frac{1}{t})-\int\frac{e^tdt}{t}=\frac{-e^t}{t}+C$
$\Rightarrow
M=\frac{-e^t}{t}|^3_1=e-\frac{e^3}{3}$
b) $\int
x^2e^{2x}dx=\frac{1}{2}\int x^2de^{2x}=\frac{1}{2}x^2e^{2x}-\int xe^{2x}dx$
$=\frac{1}{2}x^2e^{2x}-\frac{1}{2}xde^{2x}=\frac{1}{2}xe^{2x}(x-1)+\frac{1}{2}\int e^{2x}dx$
$=\frac{1}{2}xe^{2x}(x-1)+\frac{1}{4}e^{2x}+C$
$\Rightarrow
N=[\frac{1}{2}xe^{2x}(x-1)+\frac{1}{4}e^{2x}]|^1_0=\frac{1}{4}(e^2-1)$