Category: How Do

Input interpretation simplify | x^(1/3) Result x^(1/3)

Input interpretation simplify | e^X Result e^X

Input interpretation simplify | (7 + 1/y)/(x – y) Partial fraction expansion (-7 x – 1)/(x (y – x)) + 1/(x y)

Input interpretation simplify | (x pi)/180 Result (pi x)/180

Input interpretation simplify | sqrt(80) Result 4 sqrt(5) Decimal approximation 8.944271909999158785636694674925104941762473438446102897083…

Input interpretation simplify | sqrt(1 + 2 x + x^2) Result sqrt((x + 1)^2) Alternate form assuming x is real abs(x + 1) Alternate form assuming x>0 x + 1

Input interpretation Calculus and Analysis > Special Functions > Radicals Topics casus irreducibilis | cube root | nested radical | nested radical constant | Newton’s iteration | nth root | principal root of unity | principal square root | Pythagoras’s constant | quadratic surd | radical | Ramanujan log-trigonometric integrals | square root | square […]

Input interpretation simplify | sqrt(1 + 2 x + x^2) Result sqrt((x + 1)^2) Alternate form assuming x is real abs(x + 1) Alternate form assuming x>0 x + 1

Input interpretation solve 2^X = 8 Result X = (log(8) + 2 i pi n)/log(2) and n element Z Real solution X = 3

Input interpretation solve (2 X) Y×4 = 0

Input 7/20 Exact result 7/20 (irreducible) Decimal form 0.35 Percentage 35% Prime factorization 2^(-2)×5^(-1)×7 Continued fraction [0; 2, 1, 6] Egyptian fraction expansion 1/3 + 1/60 Occurrence in convergents pi/9~~0, 1/2, 1/3, 7/20, 15/43, 22/63, … (simple continued fraction convergent sequence)

Input interpretation complete the square | 28 + 10 x + x^2 Result (x + 5)^2 + 3 Geometric figure parabola Polynomial discriminant Delta = -12 Derivative d/dx((x + 5)^2 + 3) = 2 (x + 5) Indefinite integral integral (3 + (5 + x)^2) dx = x^3/3 + 5 x^2 + 28 x + […]