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PROBLEM.SM
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1993-11-15
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# Examples come from the Problem.TXT file.
output:=basic
# example 1
inte(exp(-a*x^2), x from 0 to inf)
assume(a > 0)
inte(exp(-a*x^2), x from 0 to inf)
# example 2
assume(1+n > 0)
inte(x^n, x from 0 to 1)
# example 3
subs(inte(x^n, x from eps to 1), eps=0)
# example 4
assume(n > 0)
0^n, 0^m
0^0
# example 5
lim(inte(x^k,x), k=-1)
# example 6
lim(x^k/exp(x), x=inf)
lim(x^(10^10)/exp(x), x=inf)
# example 7
inte(x^n*exp(-x), x from 0 to inf)
# example 8
inte(1/x, x from -1 to 1)
inte(1/x, x from -1 to 2)
# example 9
inte(tan(x), x from 0 to pi)
# example 10
inte(sign(x), x from -2 to 2)
inte(sign(x), x from -1 to 2)
# example 11
expand := on
inte(y'(x)*(1+1/y(x)) = -1, x)
dsolve(y'(x) = -y(x)/(y(x)+1), y(x),x)
expand := off
# example 12
dsolve(y'(x) = sqrt(y(x)), y(x),x)
y'(x) = sqrt(y(x))
last/sqrt(y(x))
inte(last,x)
# example 13
assume(p > 0, q < 0)
sqrt(p^2),sqrt(q^2),sqrt(x^2)
last
# example 14
inte(abs(x), x from -1 to 1)
inte(abs(x)^5,x)
# problem 3
inte(1/x^2, x from -3 to 1)
# problem 11
inte(1/(x+1)^3, x from -2 to 2)
# problem 12
inte(x^(-4/3), x from -1 to 1)
# problem 15
inte(1/x, x from -1 to 2)
# problem 16
inte(1/(x^2-x-2), x from 0 to 4)
# problem 22
inte(1/(x*ln(x)^2), x from 1/e to e)
# problem 23
inte(1/x^2*cos(1/x), x,-1,0,2)
# problem 29
inte(1/(x-4)^2, x from 0 to 4 to inf)
# problem 30
inte(1/(x+2), x from -inf to 0)
num(last)