Trig substitution ∫(4x^3)/√(x^2+4)

  • Thread starter bbroocks
  • Start date
  • #1
1
0

Homework Statement



∫(4x^3)/√(x^2+4)dx

Homework Equations





The Attempt at a Solution



So, I let x= 2tanθ
dx= 2sec^2θ dθ
So, √(4tan^2(θ)+4)=2secθ
∫(4x^3)/√(x^2+4)dx=∫((32tan^3(θ))/(2secθ))2sec^2(θ)dθ.

Would it go to ∫16tan^3(θ)2sec(θ)dθ
or ∫32tan^3(θ)sec(θ)dθ
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,911

Homework Statement



∫(4x^3)/√(x^2+4)dx

Homework Equations





The Attempt at a Solution



So, I let x= 2tanθ
dx= 2sec^2θ dθ
So, √(4tan^2(θ)+4)=2secθ
∫(4x^3)/√(x^2+4)dx=∫((32tan^3(θ))/(2secθ))2sec^2(θ)dθ.

Would it go to ∫16tan^3(θ)2sec(θ)dθ
or ∫32tan^3(θ)sec(θ)dθ

It is correct so far.

ehild
 
  • #3
Dick
Science Advisor
Homework Helper
26,260
619
I don't think you really need a trig substitution here. Try u=x^2+4 first.
 

Related Threads on Trig substitution ∫(4x^3)/√(x^2+4)

Replies
10
Views
9K
  • Last Post
Replies
5
Views
5K
  • Last Post
Replies
1
Views
195
  • Last Post
Replies
16
Views
7K
  • Last Post
Replies
7
Views
3K
Replies
11
Views
2K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
6
Views
7K
  • Last Post
Replies
10
Views
24K
Top