# Double exponential integration (a,∞) Calculator

## Calculates the integral of the given function f(x) over the semi-infinite interval (a,∞) using the Double exponential formula.

 This method is suitable for the function with algebraic decay at infinity.The integrand f(x) is assumed to be analytic and non-periodic except for the endpoint.
f(x)
a
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Double\ exponential\ integration\\(1)\ x\rightarrow e^{{\normal\frac{\pi}{2}}sinh(t)}\\\ {\large\int_{\tiny a}^{\hspace{25}\tiny\infty}}f(x)dx={\large\int_{\tiny 0}^{\hspace{25}\tiny\infty}}f(x+a)dx={\large\int_{\tiny -\infty}^{\hspace{25}\tiny\infty}}f(x(t)+a)x'(t)dt\\\hspace{140}x(t)=e^{{\normal\frac{\pi}{2}}sinh(t)}\\\hspace{140}x'(t)=e^{{\normal\frac{\pi}{2}}sinh(t)}\frac{\pi}{2}cosh(t)\\[10](2)\ Trapezoid\\\hspace{20}S\simeq{\large\int_{-t_a}^{\hspace{25}t_a}}f(x(t))x'(t)dt=h{\large\sum_{{\small j=-}\frac{N}{2}}^{\frac{N}{2}}}f(x(jh))x'(jh)\\\hspace{240}h={\large\frac{2t_a}{N}}\\$

Sending completion

To improve this 'Double exponential integration (a,∞) Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?
{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 1, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7961257696151733, "perplexity": 6052.57975353291}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "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": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395166.84/warc/CC-MAIN-20160624154955-00089-ip-10-164-35-72.ec2.internal.warc.gz"}