# Calc

posted by .

Use substitution to evaluate the indefinite integral:

The integral of [ (sq. root (1 + ln x)) ((ln x)/x) dx]

Im confused on what i should substitute u and du for.

Thank you so much!!

• Calc -

Let u = 1+ln x
so,
du = 1/x dx
ln x = u-1

So, we have

u^1/2 * (u-1) du
= u^3/2 - u^1/2 du

Integrate that to get

2/5 u^5/2 - 2/3 u^3/2
=
2/5 (1 + ln x)^5/2 - 2/3 (1+ln x)^3/2

Check your work by taking the derivative. Trust me -- it comes out right.

## Similar Questions

Evaluate each indefinite integral. Use the substitution method. X square root (x+3) dx
2. ### 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 …
3. ### Calc 121

How do you integrate using substitution: the integral from 1 to 3 of: ((3x^2)+(2))/((x^3)+(2x)) There is a trick to this one that grealy simplifies the integral. Let u = x^3 + 2x. Then du = (3x^2 + 2)dx The integral then bemoces just …
4. ### Calculus

"Evaluate the following indefinite integrals: "S" (3x^2 -2)/(x^3 - 2x + 1)^3 dx" We're practicing the substitution rule, and I know how to do it, but I don't know what/how to substitute in this question. btw: "S" is the integral sign.
5. ### Calc.

Evaluate the indefinite integral. Please check my work?
6. ### 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 …
7. ### Calc BC

1. Find the indefinite integral. Indefinite integral tan^3(pix/7)sec^2(pix/7)dx 2. Find the indefinite integral by making the substitution x=3tan(theta). Indefinite integral x*sqrt(9+x^2)dx 3. Find the indefinite integral. Indefinite …
8. ### math

Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral 2(2x+6)^5 dx, u=2x+6
9. ### math

Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral cos(9x) dx, u=9x