Math
posted by Dave
Evaluate the integral of e^(1/x) / x^2 from [1,2].
I let u =1/x, but then I am stuck because I am not sure what is the derivative of 1/x is?
The answer in the book is e sqrt(e)

Steve
let u=1/x
du = 1/x^2 dx
∫e^(1/x)/x^2 dx
= ∫e^u du
= e^u = e^(1/x) [1,2]
= e^(1/2) + e^(1/1)
...
Respond to this Question
Similar Questions

trig integration
s integral endpoints are 0 and pi/2 i need to find the integral of sin^2 (2x) dx. i know that the answer is pi/4, but im not sure how to get to it. i know: s sin^2(2x)dx= 1/2 [1cos (4x)] dx, but then i'm confused. The indefinite … 
Math
Hi, I need urgent help with these 3 integrals problems ... been stuck on the questions and the deadline is Friday. Thanks a lot ! 1) For the green's theorem, Q: Using Green's theorem, evaluate the line integral F(r).dr counterclockwise … 
calculus
evaluate integral or state that it is diverges integral oo, 2 [2/(x^21)] dx  integral oo, 2 [2/(x^21)] dx Through partial fractions, I came up with lim [ln(x1)ln(x+1)] b, 2 b>oo I get … 
calc II
Express the integrals as the sum of partial fractions and evaluate the integral: (integral of) (x^2)dx/(x1)(x^2 +2x+1) My work: The above integral is equal to x^2dx/(x+1)^2 (A/x1) + (B/x+1) + (Cx+D)/(x+1)^2 = x^2 A(x+1)^2 + B(x1)(x+1) … 
Calc.
Evaluate the indefinite integral. Please check my work? 
Math
1) evaluate: integral of (3x^2 + 5x  1 + 3/x) dx x^3/3 + x^2/5  x Is this correct? 
Math
1. Evaluate the indefinite integral ([6x^2 + 12x^(3/2) +4x+9]/sqrt x)dx. Answer = + C 2. Evaluate the indefinite integral (12sin x+4tan x)dx. Answer = + C 3. Evaluate the indefinite integral. (x^7)e^(x^8)dx. Answer = + C Thank you … 
Calculus prince@18
let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that … 
Math (Definite Integrals)
Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2  x^2) dx r While I recognize that this looks similar to a circle function, I'm not … 
Math
Evaluate the integral of 5^t * sin (5^t) *dt I started out with u = 5^t , but then I got stuck on du because I am not sure how to take the derivative of 5^t?