Integral: Solving (sec(10x)^2)*(tan(10x)^6)dx

  • Thread starter Thread starter Loppyfoot
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary
The integral of (sec(10x)^2)*(tan(10x)^6)dx can be approached using substitution. By letting u = tan(10x), the derivative sec^2(10x)dx can be utilized to simplify the integral. This substitution helps manage the powers of tan and sec in the expression. The discussion highlights the challenge posed by the powers in the integral and suggests a strategic method to solve it. Overall, using the substitution method is key to simplifying and solving the integral effectively.
Loppyfoot
Messages
192
Reaction score
0

Homework Statement



Integral of (sec(10x)^2)*(tan(10x)^6)dx

Homework Equations





The Attempt at a Solution



The powers are throwing me off a little bit. I realize that the derivative of tan is sec^2, bt how will that help me with this problem?
 
Physics news on Phys.org
Loppyfoot said:

Homework Statement



Integral of (sec(10x)^2)*(tan(10x)^6)dx

Homework Equations





The Attempt at a Solution



The powers are throwing me off a little bit. I realize that the derivative of tan is sec^2, bt how will that help me with this problem?

Try u = tan(10x).
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
How to Integrate 1/sqrt(1+x^2) dx | Step-by-Step Solution
  • · Replies 3 ·
Replies
3
Views
3K
Taking the root of sec^2 in an integral
  • · Replies 5 ·
Replies
5
Views
1K
Can you handle this integration with limits problem?
  • · Replies 3 ·
Replies
3
Views
2K
How Do You Integrate tan^3(9x)?
  • · Replies 3 ·
Replies
3
Views
2K
How Do You Integrate tan²x sec^4x dx?
  • · Replies 2 ·
Replies
2
Views
3K
Integral of tan^n (x), reduction fromula?
  • · Replies 1 ·
Replies
1
Views
10K
Derivative of Secant: Find dy/dx
  • · Replies 2 ·
Replies
2
Views
1K
Solve Integration Problem: tan θ sec θ → (1/2)ln(3/2)
  • · Replies 12 ·
Replies
12
Views
2K
Integrating dx / (4+x^2)^2 using Trigonometric Substitution
  • · Replies 9 ·
Replies
9
Views
2K