Chủ đề này có 1 trả lời

[lammyduyen]

$1) \int \frac{2e^{x}dx}{5e^{x}+1}   2) \int_{\frac{1}{2}}^{2}\sqrt{x^{2}+\frac{1}{x^{2}}-2}dx$

[E. Galois]

$1)$

$$\int \frac{2e^{x}dx}{5e^{x}+1} = \int \frac{2de^{x}}{5e^{x}+1} = \frac{2}{5} \ln |5e^{x}+1| +C$$

 

$2)$

$$\int_{\frac{1}{2}}^{2}\sqrt{x^{2}+\frac{1}{x^{2}}-2}dx = \int_{\frac{1}{2}}^{2}\left( x- \frac{1}{x} \right) dx= \left. \left( \frac{x^2}{2} - \ln x \right) \right|_{\frac{1}{2}}^2 = \frac{15}{16} - 2\ln 2$$