Question

Integral de e^((x+2)^1/2)
∫e^((x+2)^1/2) dx

Answer 1

∫e^(√(x+2)) dx
Sea t= √(x+2)
t² = x+2
2t dt/dx = 1
2t dt = dx

∫e^t *2t dt 
Recordemos que:
∫u dv = uv - ∫v du

Sea u= 2t
du/dt= 2
du= 2dt

Sea dv= e^t dt
∫dv = ∫ e^t dt
v= e^t
∫e^t *2t dt = 2t e^t - ∫e^t 2dt
= 2t e^t - 2∫e^t dt
= 2t e^t - 2 e^t +c
= 2e^t(t - 1) + c
= 2 e^(√(x+2)) (√(x+2) - 1) + c