March 2, 2015

Homework Help: Calculus URGENT test tonight

Posted by Gabriela on Friday, April 20, 2007 at 3:59pm.

Integral of:

(sqrt(x)+1)^2 dx

The answer is:

2ln abs(1+sqrt(x)) + 2(1+sqrt(X))^-1 +c

I have no clue why that is! Please help.

I used substitution and made u= sqrt(x)+1

but i don't know what happened along the way!

Your first step was a good one.
next, let u = sqrt x + 1
Then sqrt x = u-1
x = u^2 - u + 1
dx = 2u du - du
Therefore the integral becomes
(Integral of) (2/u) du - 2/u^2 du
= 2 ln u + 2/u +c
Finally, substitute sqrt x +1 for u

When you use substitution, both the integrand (f(x)) and the differential (dx) must be changed.

thank you so very very much!

I made a mistake with two lines, bit it came out OK.
I should have written
x = u^2 - 2u + 1
dx = 2u du - 2 du

Answer this Question

First Name:
School Subject:

Related Questions

Calculus - so we are doing integrals and I have this question on my assignment ...
Inequality - When I solve the inquality 2x^2 - 6 < 0, I get x < + or - ...
Math Help please!! - Could someone show me how to solve these problems step by ...
Calculus - Evaluate the indefinite integral: 8x-x^2. I got this but I the ...
Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...
math calculus please help! - l = lim as x approaches 0 of x/(the square root of...
Calculus - Find the volume of the solid whose base is the region in the xy-plane...
calculus - Calculate definite integral of dx/(x^4 * sqrt(x^2 + 3)) Over (1,3) I ...
Math(Roots) - sqrt(24) *I don't really get this stuff.Can somebody please help ...
Calculus - Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t...