Integral Calculus - Trigonometric Substitution

  • Thread starter Myung
  • Start date
  • #1
42
0

Homework Statement


2
∫ dx / (x+1)√[2x(x+2)]
1

Homework Equations



Let x = tan θ if √(a^2 + x^2)
Where a = constant

The Attempt at a Solution



2
∫ dx / (x+1)√(2x)√(x+2)
1

2
1/√2 ( ∫ dx / (√x)(x+1)[√(x+2)]
1

Now make all x in terms of √x so we can apply relevant equation ( applied also to constant )

2
1/√2 ( ∫ dx / (√x)((√x)^2+1)[√(√x+2)]
1

Now before i go on I want to ask if this is possible so I can apply the rule of the tangent in substitution?
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
how about noticing that
[tex] 2x(x+2) = 2(x^2+2x) =2(x^2+2x+1-1) = 2((x+1)^2-1) [/tex]
 

Related Threads on Integral Calculus - Trigonometric Substitution

Replies
9
Views
2K
Replies
3
Views
752
Replies
5
Views
3K
Replies
3
Views
3K
Replies
12
Views
6K
Replies
4
Views
1K
Replies
2
Views
2K
Replies
9
Views
2K
Replies
4
Views
2K
Replies
11
Views
538
Top