Evaluate the definite integral.

Question

Evaluate the definite integral.

2

(e^{1/x^5}/x⁶) dx

1

Answer 1

Let use substitution; u = 1/x⁵.

then du = - 5/x⁶dx, and 1/x⁶dx = - 1/5du; If x = 1 then u = 1, if x = 2 then u =1/32.

Now ∫₁²e^{1/x^5}/x⁶dx = -1/5∫₁^1/32e^udu = -1/5e^u₁^1/32 = -1/5(e^1/32 - e) ≈ 0.3373