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ja sam se zaljubilaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa 





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ja sam se zaljubilaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa![]()

Sto cinis djevojko .... 



sqrt(x) = t
dt=1/2sqrt(x) dx
Otuda se dobija da je početni integral isto što i:
2 int (t^2/ (t^2 + 1)) dt
Dodavanjem i oduzimanjem 1 u brojiocu:
2 int ((t^2+1-1)/ (t^2 + 1)) dt = 2 int dt - 2 int 1/ (t^2 +1)= 2t -2 arctg t
Vraćanjem vrednosti iz smene:
2 sqrt(x) - 2 arctg (sqrt (x))
int (ln x / (x (ln (x^2) + 1)) dx
ln x^2 = 2 ln x
int (ln x / (x (2ln x + 1)) dx
Smena ln x= t.
dt=dx / x
dx=x dt
Sledi:
int (t/ (x (2t + 1)) x* dt
int (t/(2t+1)) dt
1/2 * int (t/(t+1/2)) dt = 1/2 * int ((t+1/2 - 1/2) / (t + 1/2)) dt = 1/2 int dt - 1/4 int (1/(t+1/2) dt = 1/2 t - 1/4 ln (1+t/2)

