diff --git a/data/mathematics/integration_rules.json b/data/mathematics/integration_rules.json index 4a162324..4ffab9e3 100644 --- a/data/mathematics/integration_rules.json +++ b/data/mathematics/integration_rules.json @@ -1,53 +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)" - ] - }