Question

Решите интергал, даю 15 баллов

Answer 1

$\int (\sqrt[n]{x}+\sqrt[m]{x})\, dx=\int \sqrt[n]{x}\, dx+\int \sqrt[m]{x}\, dx=\int x^{1/n}\, dx+\int x^{1/m}\, dx=\\\\\\=\dfrac{x^{\frac{1}{n}+1}}{\frac{1}{n}+1} +\dfrac{x^{\frac{1}{m}}+1}{\frac{1}{m}+1}+C=\dfrac{n\cdot x^{\frac{n+1}{n}}}{n+1}+\dfrac{m\cdot x^{\frac{m+1}{m}}}{m+1}+C=\\\\\\=\dfrac{n\cdot \sqrt[n]{x^{n+1}}}{n+1}+\dfrac{m\cdot \sqrt[m]{x^{m+1}}}{m+1}+C$