Integration Under the Integral Sign

Author

Eric W. Weisstein
February 7, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/IntegrationUndertheIntegralSign.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/IntegrationUndertheIntegralSign.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Example

v5.0.1

Integrate[(x^α),{x,0,1}]

Integrate[(((x^b)-(x^a))/(Log[x])),{x,0,1}]//Timing

Integrate[(((x^b)-(x^a))/(Log[x])),{x,0,1},Assumptions->Re[a]>-1&&Re[b]>-1]//Timing

v5.1

Integrate[(x^α),{x,0,1}]

Integrate[(((x^b)-(x^a))/(Log[x])),{x,0,1}]//Timing

Integrate[(((x^b)-(x^a))/(Log[x])),{x,0,1},Assumptions->Re[a]>-1&&Re[b]>-1]//Timing

v6

Integrate[(x^α),{x,0,1}]

Integrate[(((x^b)-(x^a))/(Log[x])),{x,0,1}]//Timing

Integrate[(((x^b)-(x^a))/(Log[x])),{x,0,1},Assumptions->Re[a]>-1&&Re[b]>-1]//Timing