Question

Integrala din 2/x^3 - 5/x^4 dx. Imi poate explica cineva pasii va rog?

Answer 1

$\text{Primul pas: Despartim in doua integrale }:\\\displaystyle \int \left(\dfrac{2}{x^3}-\dfrac{5}{x^4}\right) dx=\int \dfrac{2}{x^3}dx-\int \dfrac{5}{x^4} dx\\\text{Pasul numarul 2: Aducem la o forma mai simpla:}\\\\int \dfrac{2}{x^3}dx-\int \dfrac{5}{x^4} dx = 2\int \dfrac{1}{x^3}dx-5\int \dfrac{1}{x^4}dx=2\int x^{-3} dx-5\int x^{-4}dx\\\text{Pasul numarul 3:Rezolvarea propriu-zisa:}\\2\int x^{-3} dx-5\int x^{-4}dx= 2\cdot \dfrac{x^{-3+1}}{-3+1}-5\cdot \dfrac{x^{-4+1}}{-4+1}+C=$

$=2\cdot \dfrac{x^{-2}}{-2} -5\cdot \dfrac{x^{-3}}{-3}+C= -x^{-2}+\dfrac{5}{3}\cdot x^{-3}+C$