Can the Integral of x*sin(x)^-1 be Solved using the Li Function?

KingNothing · Oct 15, 2006

How does one solve this integral?
[tex] \int {x * \left( {\sin x} \right)} ^{ - 1} dx[/tex]

Zelos · Oct 15, 2006

http://integrals.wolfram.com/index.jsp"
using that

arildno · Oct 15, 2006

By numerical means, i would presume.

KingNothing · Oct 15, 2006

I would appreciate some sincere responses on how to solve it, by hand.

HallsofIvy · Oct 15, 2006

You were given two "sincere" responses. The "anti-derivative" of that is not an "elementary" function. According to the web-site Zelos gave you that involves the "Li" function.

Can the Integral of x*sin(x)^-1 be Solved using the Li Function?

Discussion

Undergrad Why ##a^0=1##?

Undergrad Finding the minimum distance between two curves

High School Arc Length for Hyperbolic Sin

Undergrad Best way to numerically solve this system of equations?

Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

Graduate About ellipticity and a proof that a system of PDEs is elliptic

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Can the Integral of x*sin(x)^-1 be Solved using the Li Function?

Discussion

Similar threads

Undergrad Why is the integral of ##\arcsin(\sin(x))## so divisive?

Graduate How can the difficult Gaussian integral be solved using standard tricks?

What is the Integral of Sin(x)/(x^2+1) from -1 to 1?

Graduate Can the integral be evaluated without Mathematica?

Can the Derivative of the Function $xe^x\csc{x}$ Be Solved Using the Chain Rule?

Undergrad How can the integral of exp (-1/x) be solved?

Graduate How can the integral of exp(-x^n) be proven using polar coordinates?

Graduate Can the Integration of 1/sin(x)e^(csc^2(x)) be Solved?

Graduate Fourier, square sign wave, f(x)sin(kx) integration

Graduate Solving Integral for A: {\int}^{\pi}_{0}A(x)sin(x) exp(-bsin(x)^{2})dx=1