Integration and Differentiation

Integrate over the variable x

Integrate[1/(x^4-a^4),x]

Differentiate  the expression after Integration to the 
variable x

D[%,x]

Collect the terms

Simplify[%]

Other Integrals,note that  Mathematica  can even integrate 
over Infinity

Integrate[1/Sqrt[5-x^4],x]

NIntegrate[1/Sqrt[5-x^4],{x,0,1}]

Integrate[a Exp[-x],{x, 0,Infinity}]

Integration in more then 1 dimension

Integrate[Exp[-(x^2 +y^2)],x,y]

How does the Error function look like?