Worked Integral
Type an integrand and antidifferentiate it one rule at a time . When a
substitution is needed, the page writes out which u it chose and why
— that choice is the whole of the technique.
Try to name u before you press the button.
Carrying out the substitution is the easy half.
Write it as you would say it: 2x cos(x^2), x^5,
1/x, sin(x)^3 cos(x), x/(x^2+1),
1/(x^2+4), x sqrt(2x+1).
power
sum
substitution
inside a power
on the bottom
arctan
backwards
Worked Integral
Type any integrand of one variable. The page antidifferentiates it the way
you would on paper: one rule per line, with the rule named beside the line
that used it.
Where the constant comes from
An integral is not equal to an antiderivative. It is equal to an
antiderivative plus a constant , so + C appears on the exact line where the last integral sign
disappears — not at the end as an afterthought. Lines that still carry an
integral sign never show it, because the constant has not been earned yet.
Substitution is a choice, so it is written down
The page could integrate x
is not allowed. So nothing composite is looked up: the substitution is
named, du is worked out, and the integral is rewritten in u
before anything is integrated.
Each substitution line says what u is and what made it the one to
try — the rest of the integrand being exactly du . The x goes
back in as its own labelled line at the end, because forgetting that step
is how a correct substitution still earns no marks.
How far it goes
Up to and including substitution: the table, sums, constant multiples,
multiplying out, and a change of variable. That is the Calculus 1 toolkit.
Beyond it, the page says which technique the integral needs —
integration by parts , partial fractions ,
trigonometric substitution — and stops. Those are Calculus 2. If you
get one of those messages your setup was most likely fine; the obstacle is
a method you have not met yet.
Some integrands,
If your answer looks different
Two antiderivatives of the same function can differ by a constant and by a
great deal of algebra, so a correct answer need not match the last line
here. Check My Answer compares two
answers numerically and will settle it.
Putting this in a slide or a page
?f=2x cos(x^2)&embed=true&steps=all&controls=none
gives the finished working with no input box. Leave steps off
and the class advances it a line at a time. See
docs/url-api.md for every parameter.
Keyboard
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