# Integrands (Sage syntax, in x) of a first-year calculus course: powers,
# exponentials and logs, trigonometric and inverse trigonometric functions,
# substitution, integration by parts, partial fractions, trigonometric
# powers, square roots of quadratics, hyperbolic functions.
# make_integrals.py runs Maxima (what Sage's integrate calls) on each.
x^5
3*x^2 - 2*x + 7
(x + 1)^3
sqrt(x)
1/sqrt(x)
x^(2/3)
1/x^3
(2*x + 1)^5
sqrt(3*x + 2)
1/(2*x + 1)
1/(1 - x)
x^2*(x^3 + 1)^4
x/(x^2 + 1)
x*sqrt(x^2 + 1)
x/sqrt(1 - x^2)
(x + 1)/(x^2 + 2*x + 5)
exp(x)
exp(3*x)
exp(-x)
2^x
x*exp(x^2)
exp(x)/(1 + exp(x))
exp(sqrt(x))/sqrt(x)
log(x)
log(x)/x
1/(x*log(x))
log(x)^2/x
x*log(x)
x^2*log(x)
log(x)^2
log(2*x + 1)
sin(x)
cos(x)
sin(3*x)
cos(2*x + 1)
tan(x)
cot(x)
sec(x)
csc(x)
sec(x)^2
csc(x)^2
sec(x)*tan(x)
csc(x)*cot(x)
sin(x)*cos(x)
sin(x)^2
cos(x)^2
sin(x)^3
cos(x)^3
sin(x)^2*cos(x)
sin(x)*cos(x)^2
sin(x)^2*cos(x)^2
sin(x)^4
cos(x)^4
sin(x)^5
sin(x)^3*cos(x)^2
tan(x)^2
tan(x)^3
sec(x)^3
sin(2*x)*cos(3*x)
sin(x)*sin(2*x)
cos(x)*cos(3*x)
cos(x)/sin(x)^2
sin(x)/cos(x)^3
cos(x)*exp(sin(x))
sin(x)/(1 + cos(x))
cos(x)/(1 + sin(x)^2)
x*sin(x)
x*cos(x)
x^2*sin(x)
x^2*cos(2*x)
x*exp(x)
x^2*exp(x)
x^3*exp(x)
x*exp(-x)
x*exp(2*x)
exp(x)*sin(x)
exp(x)*cos(x)
exp(2*x)*sin(3*x)
x*sinh(x)
arctan(x)
arcsin(x)
arccos(x)
x*arctan(x)
x*arcsin(x)
1/(1 + x^2)
1/(4 + x^2)
1/(1 + 4*x^2)
1/sqrt(1 - x^2)
1/sqrt(4 - x^2)
1/sqrt(1 + x^2)
1/sqrt(x^2 - 1)
1/sqrt(x^2 + 4)
sqrt(1 - x^2)
sqrt(4 - x^2)
sqrt(1 + x^2)
sqrt(x^2 - 1)
1/(1 - x^2)^(3/2)
1/(x^2 + 1)^(3/2)
x^2/sqrt(1 - x^2)
1/(x^2 - 1)
1/(x^2 - 4)
1/(x*(x + 1))
1/((x - 1)*(x + 2))
(3*x + 1)/(x^2 - x - 2)
x/((x - 1)*(x - 2))
x^2/(x - 1)
(x^3 + 1)/(x + 1)
x^3/(x^2 + 1)
1/(x^2 + x + 1)
1/(x^2 + 2*x + 2)
(2*x + 3)/(x^2 + 2*x + 2)
1/(x^3 + 1)
1/(x^3 - 1)
x/(x^3 - 1)
1/(x^4 - 1)
1/(x^4 + 1)
1/(x*(x^2 + 1))
1/(x^2*(x + 1))
1/(x + 1)^2
x/(x + 1)^2
1/(x^2 + 1)^2
x/(x^2 + 1)^2
1/((x^2 + 1)*(x^2 + 4))
(x^2 + 1)/(x^4 + x^2)
(5*x^2 + 3*x - 2)/(x^3 + 2*x^2)
1/(x^2 - 2)
1/(x^2 - 2*x - 1)
1/(x^3 - 2)
sinh(x)
cosh(x)
tanh(x)
sinh(x)^2
cosh(x)^2
sech(x)^2
x*cosh(x)
exp(x)*sinh(x)
1/(exp(x) + 1)
exp(2*x)/(exp(x) + 1)
1/(exp(x) + exp(-x))
exp(x)/(exp(2*x) + 1)
(1 + x)*exp(x)
(x^2 + 1)*exp(-x)
sin(x)^2/cos(x)
sec(x)^4
tan(x)*sec(x)^2
tan(x)^2*sec(x)^2
sin(sqrt(x))
x/(1 + x^4)
x^3/sqrt(1 + x^2)
1/(x*sqrt(x^2 - 1))
1/(x^2*sqrt(1 - x^2))
1/(1 + sqrt(x))
sqrt(x)/(1 + x)
x*(x + 1)^10
(log(x) + 1)*x^x
sin(log(x))
cos(x)*sin(x)^4
exp(x)*sqrt(1 + exp(x))
arctan(x)/(1 + x^2)
arcsin(x)/sqrt(1 - x^2)
sin(x)*cos(x)/(1 + sin(x)^2)
x*exp(x)*sin(x)
1/(sin(x) + cos(x))
1/(1 + cos(x))
1/(2 + cos(x))
exp(x^2)
sin(x)/x
sin(x^2)
exp(-x^2)
1/log(x)
sqrt(1 + x^3)
