Selected Homework 10

Int(1/(x^2),x = 1 .. infinity) = Limit(Int(1/(x^2),x = 1 .. b),b = infinity)




Int(1/x,x = 1 .. infinity) = Limit(Int(1/x,x = 1 .. b),b = infinity)




Int(exp(-x),x = 0 .. infinity) = Limit(Int(exp(-x),x = 0 .. b),b = infinity)




Int(1/(x^2+1),x = 0 .. infinity) = Limit(Int(1/(x^2+1),x = 0 .. b),b = infinity)




Int(sin(x),x = 0 .. infinity) = Limit(Int(sin(x),x = 0 .. b),b = infinity)




Int((1-x)*exp(-x),x = 1 .. infinity) = Limit(Int((1-x)*exp(-x),x = 1 .. b),b = infinity)




Int(exp(x)/(1+exp(2*x)),x = -infinity .. infinity) = Limit(Int(exp(x)/(1+exp(2*x)),x = a .. c),a = -infinity)+Limit(Int(exp(x)/(1+exp(2*x)),x = c .. b),b = infinity)




Int(ln(x),x = 0 .. exp(1)) = ``




Int(1/((x-2)^(1/2)),x = 2 .. 5) = ``




Int(sec(x),x = 0 .. 1/2*Pi) = ``




Int(1/(x-1),x = 0 .. 3) = ``



Int(1/(x^(1/2)*(1+x)),x = 0 .. infinity) = ``




Int(1/(x^2+4),x = -infinity .. infinity) = ``




Int(cos(x)/sin(x)^(1/2),x = 0 .. 1/4*Pi) = ``