Răspuns:
Explicație pas cu pas:
Aici jmenul era sa amplifici functia cu x²⁰¹⁴.
[tex]\displaystyle \int\dfrac{dx}{x\cdot(x^{2015}+1)}=\int\dfrac{x^{2014}}{x^{2015}\cdot (x^{2015}+1)}dx=\dfrac{1}{2015}\cdot\int\dfrac{2015x^{2014}}{x^{2015}(x^{2015}+1)}dx\\x^{2015}=t\Rightarrow 2015x^{2014} dx=dt\\=\dfrac{1}{2015}\int\dfrac{1}{t(t+1)}dt=\dfrac{1}{2015}\int\dfrac{t+1-t}{t(t+1)}dt=\dfrac{1}{2015}\left(\int\dfrac{1}{t}dt-\int\dfrac{1}{t+1}dt\right)\\=\dfrac{1}{2015}(\ln(t)-\ln(t+1))=\dfrac{1}{2015}\cdot \ln\left(\dfrac{t}{t+1}\right)=\dfrac{1}{2015}\cdot \ln\left(\dfrac{x^{2015}}{1+x^{2015}}\right)+c[/tex]
Raspunsul corect este e.
