Integral of sin(2x+3)/(x^2+3x-2)

This integral cannot be evaluated.In summary, the conversation discusses a specific integral and the speaker is unable to find a solution for it due to the numerator and denominator being related in a complex way.
  • #1
Astudious
61
0
Is there any way of evaluating the following integral:

[tex]\int sin{(\frac{2x+3}{x^2+3x-2})} dx[/tex]

I have thought hard but cannot find an answer.

Obviously, the denominator is the differential of the numerator. But a function is being taken of this fraction...
 
Physics news on Phys.org
  • #2
Astudious said:
Is there any way of evaluating the following integral:
I doubt it.
Astudious said:
[tex]\int sin{(\frac{2x+3}{x^2+3x-2})} dx[/tex]

I have thought hard but cannot find an answer.

Obviously, the denominator is the differential of the numerator. But a function is being taken of this fraction...
No, the numerator (top) is the differential of the denominator (bottom).
 

1. What is the integral of sin(2x+3)/(x^2+3x-2)?

The integral of sin(2x+3)/(x^2+3x-2) is a complex integral that involves using substitution and integration by parts to solve. The final answer is a combination of trigonometric functions and natural logarithms.

2. Is there a simpler form for the integral of sin(2x+3)/(x^2+3x-2)?

No, there is not a simpler form for the integral of sin(2x+3)/(x^2+3x-2). However, there are techniques that can be used to make the integration process more manageable, such as using trigonometric identities or partial fraction decomposition.

3. Can the integral of sin(2x+3)/(x^2+3x-2) be solved without using substitution?

No, substitution is necessary to solve the integral of sin(2x+3)/(x^2+3x-2). Without substitution, the integral becomes much more complicated and difficult to solve.

4. Is there a specific interval over which the integral of sin(2x+3)/(x^2+3x-2) can be evaluated?

Yes, the integral of sin(2x+3)/(x^2+3x-2) can be evaluated over any interval where the function is continuous. This would typically be over the entire real number line, unless there are discontinuities present.

5. How can the integral of sin(2x+3)/(x^2+3x-2) be applied in real-world situations?

The integral of sin(2x+3)/(x^2+3x-2) can be used in physics, engineering, and other fields to solve problems involving oscillating or periodic functions. It can also be used to calculate the area under a curve with a sinusoidal shape.

Similar threads

B Integration by parts of inverse sine, a solved exercise, some doubts...
    • Calculus
Replies
4
Views
921
I Did Math DF's integral calculator make a glaring mistake?
    • Calculus
Replies
8
Views
190
I Why is the integral of ##\arcsin(\sin(x))## so divisive?
    • Calculus
Replies
3
Views
1K
I Substitution in a definite integral
    • Calculus
Replies
6
Views
1K
B Some questions regarding the integral of cos(ax), "a" not zero
    • Calculus
Replies
16
Views
1K
I Integration of √(1-x^2) with x=sinθ: Check Correctness and Simplification
    • Calculus
Replies
12
Views
2K
I Integration of ##e^{-x^2}## with respect to ##x##
    • Calculus
Replies
4
Views
1K
B Integration by Parts, an introduction I get confused with
    • Calculus
Replies
2
Views
944
B Question about change of variables
    • Calculus
Replies
29
Views
732
A Multiplying divergent integrals using Hardy fields approach
    • Calculus
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top