Generalized integral

[bellum753]

I tried to solve these two integrals but did not succeed.
How to study the convergence?

-) Integral from 0 to +inf 1/(sqrt(x^3(abs(cosx-sinx)))) dx

-) Integral from 0 to +inf (x^3 * cosx) / ((1+x^2)^2) dx

 

[stapel]

I tried to solve these two integrals but did not succeed.

Please reply with a clear statement of your efforts, so that we may help you find where you may be going astray. Thank you!

 

[DrPhil]

I tried to solve these two integrals but did not succeed.
How to study the convergence?

-) Integral from 0 to +inf 1/(sqrt(x^3(abs(cosx-sinx)))) dx

-) Integral from 0 to +inf (x^3 * cosx) / ((1+x^2)^2) dx

You did a good job balancing the parentheses - very difficult to type equations inline. I want to write them out using LaTeX to see them better.

1) \(\displaystyle \displaystyle \int_0^\infty \dfrac{dx}{\sqrt{x^3\ \mid (\cos x - \sin x) \mid }} \)

2) \(\displaystyle \displaystyle \int_0^\infty \dfrac{x^3\ \cos{x}}{(1 + x^2)^2 } dx\)

What do you mean by "solve"? Is the question just whether the integrals converge or not? What can you learn by studying the integrands? And DO show us your work.

 

[Deleted member 4993]

It is also very enlightening to plot these functions (using graphing tool) and observe .....