Question

f:R→R, f(x)=$(x-1)*e^{-x}$


Calculati $\int\limits^e_2 {\frac{1}{f(x) * e^{x} } } \, dx$

Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle\int_2^e\dfrac{1}{f(x)\cdot e^x}dx=\int_2^e\dfrac{1}{(x-1)\cdot e^x\cdot e^{-x}}dx=\int_2^e\dfrac{1}{x-1}dx=\ln(x-1)|_2^e=\\=\ln(e-1)-\ln1=\ln(e-1)$