What is the Easiest Way to Solve an Integration Problem Involving Tan(x)?

In summary, to solve the indefinite integral, use the fact that the derivative of tan x is sec^2 x and try a u-substitution by setting u = tan(x) + 2. The solution is -(2+u)^-1 and thanks for the reply.
  • #1
Noo
26
0
Solved. Thanks.
 
Last edited:
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  • #2
The simplest way to solve that indefinite integral is to realize that

[tex]\frac{d}{dx}tan x = sec^{2}x[/tex] , and try a u-substitution from there...
 
  • #3
meiso said:
The simplest way to solve that indefinite integral is to realize that

[tex]\frac{d}{dx}tan x = sec^{2}x[/tex] , and try a u-substitution from there...

Yes, sorry, i am stupid. I realized that 2 minutes after posting here. I'm pretty sure i have it now. It's just -(2+u)^{-1} for u=tanx, right? And thanks for the reply.
 
  • #4
Noo said:
It's just -(2+u)^{-1} for u=tanx, right? And thanks for the reply.

No problem. And, actually, you can set u = tan(x) + 2 to make things even easier. 2 is just a constant, so the derivative of tan(x) is the same as the derivative of tan(x) + 2.
 

Related to What is the Easiest Way to Solve an Integration Problem Involving Tan(x)?

1. What is integration?

Integration is a mathematical process that involves finding the area under a curve. It is used to solve problems involving rates of change, such as velocity, acceleration, and growth.

2. What is a little integration problem?

A little integration problem is a simple mathematical problem that involves finding the area under a curve using integration. It is usually used to introduce students to the concept of integration and its applications.

3. How do you solve a little integration problem?

To solve a little integration problem, you need to first identify the function that represents the curve and its limits of integration. Then, you can use various integration techniques, such as substitution, integration by parts, or the fundamental theorem of calculus, to find the area under the curve.

4. What are the applications of integration?

Integration has various applications in science, engineering, economics, and other fields. It is used to solve problems involving rates of change, such as finding the distance traveled by an object with a changing velocity or determining the growth rate of a population.

5. Is integration difficult to learn?

Like any other mathematical concept, integration may seem difficult at first, but with practice and understanding of the underlying principles, it can be mastered. It is important to have a good foundation in algebra and calculus before learning integration.

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