Question

∫ 3x - 1 / x(x-1)² dx

Answer 1

Resposta:

Explicação passo-a-passo:

$\int \frac{3x-1}{x\left(x-1\right)^2}dx = \\\\=\int \frac{3x}{x\left(x-1\right)^2}dx-\int \frac{1}{x\left(x-1\right)^2}dx$

$\int \frac{3x}{x\left(x-1\right)^2}dx =\int \frac{3}{\left(x-1\right)^2}dx = -\frac{3}{x-1} }$

$\int \frac{1}{x\left(x-1\right)^2}dx = lnIxI - ln Ix - 1I - \frac{1}{x - 1}$

Então, continuando a derivada acima:

$= -\frac{3}{x-1} }-(lnIxI - ln Ix - 1I - \frac{1}{x - 1}) = \\\\= -\frac{3}{x-1} }-lnIxI + ln Ix - 1I + \frac{1}{x - 1} =\\\\= -\frac{2}{x-1} }-(lnIxI - ln Ix - 1I +c$