diff --git a/data/mathematics/integration_rules.json b/data/mathematics/integration_rules.json new file mode 100644 index 00000000..4ffab9e3 --- /dev/null +++ b/data/mathematics/integration_rules.json @@ -0,0 +1,37 @@ +{ + "description":"Integration rules for any function", + "constant": [ + "integral a dx = ax + C, where a and C are both constants" + ], + "variable": [ + "integral x dx = (x^2)/2+ C" + ], + "square": [ + "integral x^2 dx = (x^3)/3 + C" + ], + "reciprocals": [ + "integral (1/x) dx = ln|x| + C" + ], + "exponential functions": [ + "integral e^x dx = e^x + C", + "integral a^x dx = a^x/ln(a) + C", + "integral ln(x) dx = x ln(x) -x + C" + ], + "trigonometric functions":[ + "integral cos(x) dx = sin(x) + C", + "integral sin(x) dx = -cos(x) + C", + "integral sec^2(x) dx = tan(x) + C" + ], + "power":[ + "integral x^n dx = (x^(n+1)/n+1) C" + ], + "difference":[ + "integral (f - g) dx = integral f dx - integral g dx" + ], + "multiplication by constant":[ + "integral cf(x) dx = c (integral f(x) dx), where c is a constant" + ], + "parts":[ + "integral u v da = u(integral v da) - integral u`(integral v da) da; u isfunction of u(a); v is function of v(a); u` is derivative of function u(a)" + ] +}