Question

calcule a integral:
∫(t*raiz de t+raiz de t/t^2)dt

Answer 1

Resposta:

∫(t*raiz de t+raiz de t/t^2)dt

∫(t√t+√t*t⁻²) dt

∫(t√t+√t/t²) dt

∫(t^(1+1/2)+t^(1/2-2)) dt

∫(t^(3/2)+t^(-3/2) dt

=t^(3/2+1)/t^(3/2+1) +t^(-3/2+1)/(-3/2+1) + c

=t^(5/2)/(5/2) +t^(-1/2)/(-1/2) + c

=(2/5)*t^(5/2) -2t^(-1/2) + c

=(2/5)*√t⁵ -2/√t + c