Question

Encontre a primitiva de F de f que satisfaça a condição dada:

f(x) = (x^2 - 1)/(x) f(1) = 1/2

Answer 1

Resposta:

$f(x) = \frac{1}{2} x^2-ln|x|$

Explicação passo-a-passo:

$\int\limits^{}_{} {\frac{x^2-1}{x} } \, dx \\\\\int\limits^{}_{} {\frac{x^2}{x}- {\frac{1}{x} }\, dx\\\\\int\limits^{}_{} x \,dx- \int\limits^{}_{} \frac{1}{x} }\, dx\\\\= \frac{1}{2} x^2-ln|x|+c\\\\f(1)=\frac{1}{2}\\\\ f(1)= \frac{1}{2} 1^2-ln1+c=\frac{1}{2}\\\\\frac{1}{2} +c= \frac{1}{2}\\\\c=0\\\\f(x) = \frac{1}{2} x^2-ln|x|$