Monday, May 25, 2009

Wolfram Alpha in the Classroom


Indefinite integral:Show steps

integral 1/sqrt(1-x^2) dx = sin^(-1)(x)+constant
RawBoxes[RowBox[{SuperscriptBox[sin, RowBox[{-, 1}]], (, x, )}]] is the inverse sine function »

Plots of the integral:

Series expansion at x=-1:More terms

-pi/2+sqrt(2) sqrt(x+1)+(x+1)^(3/2)/(6 sqrt(2))+(3 (x+1)^(5/2))/(80 sqrt(2))+(5 (x+1)^(7/2))/(448 sqrt(2))+(35 (x+1)^(9/2))/(9216 sqrt(2))+(63 (x+1)^(11/2))/(45056 sqrt(2))+O((x+1)^(13/2))+constant

Series expansion at x=0:More terms

x+x^3/6+(3 x^5)/40+O(x^7)+constant

Series expansion at x=1:More terms

1/2 (pi+(-1)^((left floor)-(arg(x-1))/(2 pi)(right floor)) (-2 i sqrt(2) sqrt(x-1)+(i (x-1)^(3/2))/(3 sqrt(2))-(3 i (x-1)^(5/2))/(40 sqrt(2))+(5 i (x-1)^(7/2))/(224 sqrt(2))-(35 i (x-1)^(9/2))/(4608 sqrt(2))+(63 i (x-1)^(11/2))/(22528 sqrt(2))+O((x-1)^(13/2))))+constant
RawBoxes[RowBox[{arg, RowBox[{(, z, )}]}]] is the complex argument »
RawBoxes[TemplateBox[{x}, Floor]] is the floor function »

Series expansion at x=∞:More terms

1/2 (2 i log(1/x)+pi-i log(4))+i/(4 x^2)+(3 i)/(32 x^4)+(5 i)/(96 x^6)+O((1/x)^7)+constant
RawBoxes[RowBox[{log, RowBox[{(, x, )}]}]] is the natural logarithm »
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