# Integration involving product of inverse error and polynomial functions

I am stuck with the following integral: $$\int_{x \ge 1} \frac{18 \exp \left(-\frac12 \left(\phi^{-1}[1 - \frac{1}{x^3}]\phi^{-1}[1 - \frac{1}{(z-x)^3}] \right) \right)}{\sqrt{3}x^3 (z-x)^4} dx$$ where $z$ is a constant and $\phi^{-1}$ is the inverse of the standard normal cdf which can also be expressed in terms of the error function: $$\phi^{-1}[p] = \sqrt{2} \operatorname{erf}^{-1}(2p-1)\qquad\text{for}\quad p \in (0,1)$$

Can this be solved analytically or numerically?

-

3
Analytically, unlikely. Numerically... difficult, but doable I think. – J. M. Jan 3 '12 at 7:31
Where does it come from? What does cdf mean? – draks ... Apr 5 '12 at 10:48
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9174001812934875, "perplexity_flag": "head"}