Integrating x^3/(1+x^2) from 0 to 1.48766439

In summary, the conversation discusses how to solve an integral problem involving x^3/(1+x^2) from zero to 1.48766439. The individual attempting the problem tried various methods but could not find a solution. However, with the help of another individual, they were able to solve the problem by using u substitution and simplifying the equation.
  • #1
Swerting
35
0

Homework Statement


I have to take an integral of [tex]x^3/(1+x^2)[/tex] from zero to 1.48766439...(I have the number).


Homework Equations


None really.


The Attempt at a Solution


Well, I tried and tried, and I could not find a single way to separate the top from the bottom. Also, I tried u substitution of both [tex]x^3[/tex] and [tex]1+x^2[/tex] but it never seemed to work out. I'm not sure if this would be good for integration of parts, since I believe that one must be able to be integrated multiple times, such as [tex]e^x[/tex], so any nudge in the right direction would help. I have the correct answer, I just would like to be able to know how to get to it. Thank you for your time.

-Swerting
 
Last edited:
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  • #2
Try writing it as x^2*x/(1+x^2). Now substitute u=1+x^2. Replace the x^2 in the numerator by u-1. Do you see it now?
 
  • #3
Ah yes! I completely forgot about that! Thank you very much, I do believe I have it now!
 

FAQ: Integrating x^3/(1+x^2) from 0 to 1.48766439

What is the meaning of "integrating x^3/(1+x^2) from 0 to 1.48766439"?

Integrating x^3/(1+x^2) from 0 to 1.48766439 refers to finding the area under the curve of the function x^3/(1+x^2) between the x-values of 0 and 1.48766439.

Why is it necessary to integrate this specific function?

This function may be integrated for various reasons, such as determining the total amount of work done by a varying force, calculating the distance traveled by an object with a changing velocity, or finding the total charge in an electrical circuit with a changing current.

How is the integration of x^3/(1+x^2) from 0 to 1.48766439 performed?

The integration of x^3/(1+x^2) from 0 to 1.48766439 can be performed using techniques such as substitution, integration by parts, or partial fractions. The result will be expressed as a definite integral with the given limits of integration.

What is the significance of the limits of integration being 0 and 1.48766439?

The limits of integration represent the specific range of values for which the area under the curve is being calculated. In this case, the limits of 0 and 1.48766439 correspond to the x-values between which the area under the curve of the function x^3/(1+x^2) is being determined.

What is the final result of integrating x^3/(1+x^2) from 0 to 1.48766439?

The final result of integrating x^3/(1+x^2) from 0 to 1.48766439 will be a numerical value that represents the area under the curve of the function over the given range of x-values. This value can be calculated using a calculator or by hand using the appropriate integration techniques.

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