INTEGRATION

creator:  Peter Knipp
repo:  github.com/pknipp/calculus

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differentiation
root-finding
max-finding
1st order differential equations
2nd order differential equations

In the url bar after 'https://basic-calculus.herokuapp.com/integration type the following:

/<lower limit of integration>/<upper limit of integration>/<function of x>

Neither singularities (integrable or otherwise) nor infinite ranges of integration are allowed. The function may be any algebraically legal combination of the variable letter(s), numbers, parentheses, and/or binary operations +, -, *, ** (encouraged) or ^ (discouraged), PI and/or the most common unary functions: abs, acos, acosh, acot, acoth, acsc, acsch, asec, asech, asin, asinh, atan, atanh, cbrt, ceil, cos, cot, csc, exp, exp2, exp_m1, floor, fract, ln, ln_1p, log10, log2, sec, signum, sin, sqrt, tan, and trunc. (See docs for more information.) To represent division you must use either div, d, DIV or D because the usual division symbol (/) has special meaning in a url. Implied multiplication is allowed. Spaces are allowed but discouraged.
The construction rules for the values of any variable in the url are the same as those for the function except - of course - it cannot include the letter which represents the variable.
example:To integrate the function 2x + 3/(x⁴ + 5) from x = 1 to 6, type /1/6/2x+3d(x**4+5) after the current url address. The result for this should be 35.41...
algorithms: composite Simpson's rule and Aitken extrapolation
json: Type '/api' in the url bar immediately before 'integration' if you would like the result in json rather than in html. A successful response will contain five properties. 'xi' and 'xf' are the lower and upper limits of integration, 'integral' is the value of the definite integral, and 'subdivisions' is the number of equally sized intervals into which the range of integration needed to be subdivided in order to achieve the absolute accuracy specified in the last property: 'epsilon'. An unsuccessful response will have one property: 'message' (a string reporting the error)