How Do You Solve the Integral of (sec^2(sqrt(x)))/sqrt(x) Using u-Substitution?

Click For Summary
SUMMARY

The integral of \(\frac{\sec^2(\sqrt{x})}{\sqrt{x}} dx\) can be effectively solved using the substitution \(u = \sqrt{x}\). This substitution simplifies the integral significantly, allowing for easier integration. The discussion highlights the common pitfalls of choosing inappropriate substitutions and emphasizes the importance of selecting intuitive variables for u-substitution.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with u-substitution technique
  • Knowledge of trigonometric functions, specifically secant
  • Basic algebraic manipulation skills
NEXT STEPS
  • Practice solving integrals using various u-substitution techniques
  • Explore advanced integration methods, such as integration by parts
  • Learn about the properties of trigonometric integrals
  • Study the relationship between derivatives and integrals in calculus
USEFUL FOR

Students and educators in mathematics, particularly those focusing on calculus, as well as anyone looking to improve their skills in solving integrals using substitution methods.

mrdoe
Messages
36
Reaction score
0
Find
\displaystyle\int\dfrac{\sec ^2\sqrt{x}}{\sqrt{x}} dx
We're supposed to use u du substitution but I can't seem to get this one.

EDIT: Sorry I didn't read rules.

I tried u=\sec^2\sqrt{x} and all variants. Usually it was in the form of

[sec or cos][^2 or none][sqrt x]
 
Physics news on Phys.org
Well a more intuitive substitution would be to take u=\sqrt{x}.
 
thanks, I can't see why I didn't see that
 

Similar threads

Replies
3
Views
2K
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 105 ·
4
Replies
105
Views
11K
  • · Replies 27 ·
Replies
27
Views
4K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K