Inegration with square roots - calc 1

Click For Summary
SUMMARY

The integral ∫x/√(x-1)dx can be solved effectively using the substitution u=x-1. This approach simplifies the integral significantly compared to the initial substitution of u=√(x-1), which complicates the integration process. The correct substitution leads to a more manageable integral that can be solved using standard integration techniques. Aimee's suggestion to use u=x-1 is the definitive method to approach this problem.

PREREQUISITES
  • Understanding of integral calculus and basic integration techniques
  • Familiarity with substitution methods in integration
  • Knowledge of algebraic manipulation of expressions
  • Experience with handling square roots in integrals
NEXT STEPS
  • Practice solving integrals using different substitution methods
  • Explore advanced integration techniques such as integration by parts
  • Study the properties of definite and indefinite integrals
  • Learn about common integral forms and their applications
USEFUL FOR

Students studying calculus, particularly those tackling integration problems, and educators looking for effective teaching methods in integral calculus.

Aimee79
Messages
2
Reaction score
0
1. Homework Statement [/b]
∫x/√(x-1)dx

2. Homework Equations [/b]
I'm just stumped. I have tried u substituion with
u=√(x-1)
x=u^2+1

((u^2+1)/u)du
=(u+1/u)du

but it doesn't seem to work and I can't integrate 1/u.

I just don't know where to go with this any help would be greatly appreciated.

Aimee
 
Physics news on Phys.org
If I were doing this question, I wouldn't make the substitution you made, but would instead use the substitution u=x-1.
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K