Verified answer

Ola antony

∫ (x² - 1)/(x² + 1) dx = ∫ (x² - 1 - 1 + 1)/(x² + 1) dx =

∫ (x² + 1)/(x² + 1) dx - ∫ 2/(x² + 1) dx = x - 2*arctg(x) + const

pronto

∫ (x²-1) / (x²+1) dx

1-1=0 , podemos inserir sem modificar a expressão

(x²-1+1-1) / (x²+1) =(x²+1-2) / (x²+1)

=(x²+1)/(x²+1) - 2/(x+1) ..corrigi aqui

=1 - 2/(x²+1)

=∫ 1 - 2/(x²+1) dx

=∫ dx - ∫ 2/(x²+1) dx

=x +cosnt - ∫ 2/(x²+1) dx

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∫ 2/(x²+1) dx=2*arctg(x) + const

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=x -2*arctg(x) + const