# calculus

posted by .

how do you solve the integral of 1/[(square root of x)(lnx)] from 2 to infinity?
i did the p- integral theorem with 1/square root of x and got it to be a divergent integral. however i was told this was the wrong way and that i should do it by integration by parts. but i can't figure it out by that method. please help. thanks.

• calculus -

You can proceed as follows. Substitute:

x = e^t. Then the integral becomes:

Integral from ln(2) to infinity of

e^(t/2)/t dt

We can get rid of the factor 2 in the exponential by putting y = t/2. The integral becomes:

Integral from 1/2 ln(2) to infinity of

e^(y)/y dy

For positive y we have

e^(y) > 1

It follows from this that the integral is larger than

Integral from 1/2 ln(2) to infinity of

1/y dy

but this is already divergent, so the integral diverges.

## Similar Questions

1. ### Calculus

Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of (sin(3*pi*t))dt For this one, I got -1/3pi cos (9 pi^2) + 1/3pi 2. indefinite integral of sinxcos(cosx)dx I got sin(cosx) + C 3. Indefinite integral of x over (root …
2. ### Calculus

Find the exact area of the region enclosed by the square root of (x) + the square root of (y) is = 1; x = 0 and y = 0. I moved the first equation around to get: y = [1- the square root of (x) ] ^2 Unfortunately, this gives me bounds …
3. ### calculus

is this correct? use the integral test to determine if this series is convergent or divergent: the series from n=2 to infinity of 1/(n*square root of (ln(n))) I said it was divergent because the integral went to infinity
4. ### calculus

how do you determine the convergence of : definite integral from 1--> infinity of lnx/(x^3)?
5. ### Maths Calculus Derivative Integral - Urgent Please

Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 (at the top) to x-5 (at the bottom) of square root of Sin(x)dx
6. ### Calculus check

The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write, but …
7. ### Quick calc question

Which of the following integrals cannot be evaluated using a simple substitution?
8. ### Calculus

Which of the following integrals cannot be evaluated using a simple substitution?
9. ### Calculus

Which of the following integrals cannot be evaluated using a simple substitution?
10. ### Calculus

Use the Comparison Theorem to determine whether the following integral is convergent or divergent. S= integral sign b=infinity and a=1 S(9(cosx^2))/ (1+x^2) dx

More Similar Questions