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Understanding the information icons

Orange: check a warning

The orange icon highlights something to check, such as how your input was interpreted. Open it to read the warning and notation advice; if this interpretation does not match your intention, edit your input and run the calculation again.

Blue: understand a step

Next to a step, the blue icon opens additional explanations: the rule used, the details of a calculation or a clarification to help you understand the next step.

In an answer, click or tap the icon to show the details. The number in parentheses tells you how many items are available: (2) means two items. To hide them again, click or tap the information icon inside the open box.

Numerical calculation

Operations, percentages and averages

calculate 12*8 calculate 25% of 200 calculate average of 4, 8 and 12 calculate the average of 6, 12, 24 and 50 What is 23 multiplied by 9? What is the sum of 34 and 29? What is the difference between 18 and 7? What is 2 plus 3 times 4? subtract 4 from negative 8 2 times 3 over 4
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Fractions

Addition, simplification and common denominators

calculate 1/4+1/2 22 1/5 - 9 8/9 two thirds of 12 simplify 2x/4 add the fractions 4/x and (x+1)/(x-5) addfrac(x+1/x) simplify (x^2-1)/(x-1) simplify (2x^2+4x)/2x simplify x^2/x + 1/x simplify (a^3+b^3)/(b^2-a^2)
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Algebraic expressions

Simplification, expansion and algebraic identities

expand (x+1)^2 expand (2x-3)(2x+3) expand (a+b)^2 expand (x+1)^3 expand (x+3)^3 expand (x-2)(x+5) expand 3(2x-1) simplify (a^2-b^2)/(a-b) the absolute value of x-1
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Powers and roots

Exponents, square roots and nth roots

calculate 2^10 calculate square root of 144 simplify root(32,5) simplify sqrt(50) simplify sqrt(x^2) simplify x^5/x^2 simplify x^4sqrt(x^{10)}
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Exponentials and logarithms

Exponential, natural logarithm and logarithms with an explicit base

calculate log(100) calculate log(2, 8) calculate log2(8) log(2, 8) add ln(8) and ln(8) calculate exp(ln(5)) simplify ln(e^x) simplify log(3,9x)-log(3,3) calc((1+e)^2)
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Arithmetic

GCD, LCM, prime numbers, factorials, Euclidean division

calculate gcd of 24 and 36 calculate lcm of 4 and 6 factorize 8680 into prime factors factor(27880) calculate 9! 7! euclidean division of x^4+x^2-1 by x^2+1 div(x-5, (x-1)*(x-2)) euclidean division of 12 by 5 simplify (14!)/(3!(14-3)!)
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Differentiation and integration

Derivatives, antiderivatives, integrals, differential equations, Laplace transforms

differentiate x^2 differentiate x^2*e^x differentiate ln(x^2+1) differentiate sqrt(x^2+1) differentiate x*sin(x) differentiate x^n differentiate cos(2x) differentiate 1/(x+1) differentiate x*ln(x) differentiate e^(2x)
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Solving and factoring

Equations, inequalities, systems, factorizations

solve 2x+3=7 solve 2x^2+3x-2=0 solve x^2+4=0 in C solve abs(x-2)=3 solve sqrt(x)=3 solve x^3-x=0 solve ln(x)=0 solve e^x=1 solve x^2-5x+6=0 solve sin(x)=0 on [0,2*pi]
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Limits and sums

Limits, from the left and from the right, finite and infinite sums

limit x->0 sin(x)/x limit x->infinity (1+1/x)^x limit x->0+ ln(x) limit x->0 (1-cos(x))/x^2 limit x->0 (e^x-1)/x limit x->infinity ln(x)/x limit x->2 (x^2-4)/(x-2) limit x->0+ x*ln(x) limit x->infinity x^2/e^x limit of x/(x+1) when x tends to infinity
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Function analysis

Domain, parity, asymptotes, extrema, inverse, tangent

definition domain of ln(sqrt(x)) evaluate the definition domain: cos(x) dom(ln(x-1)) domain of ln(ln(x^2+2)) domain of ln(sin(x)+cos(x)+2) domain(ln(x+y)-ln(x)-ln(y)) domain(sqrt(x),y) domain(1/x,y,'C') domain(ln(sqrt(x)-2)+sqrt(x)) parity f(x)= 1/(x^2+3)
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Trigonometry

Exact values, radians and degrees, inverse functions

calculate sin(pi/6) calculate cos(60°) calculate tan(pi/4) calculate sec(60°) calculate cot(pi/4) calculate csc(30°) simplify sin(x)^2+cos(x)^2 calculate acos(sqrt(2)/2) simplify cot(x)*sin(x) calculate asin°(1/2)
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Complex numbers

Modulus, argument, exponential and polar forms

(1+i)^2 polar(2+2i) mod(3+4i) arg(3+4i) write 3+4*i in exponential form the polar form of 3+4i simplify (4+3i)/(3-2i) sqrt(-4)
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Geometry

Points, vectors, distances, midpoints, lines and slopes

coord(1,2)+coord(3,4) coord(1,2)*coord(3,4) norm(coord(3,4)) coord(1,2)/2 midpoint (-1/4 ,-1/7),(3/4 , 6/7) perpendicular 2x+5y=10 distance (-1,8),(4,-2) line (2,3),(-1,5) slope of 2y=4x+5
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Plotting

Graphs of one or several functions

draw f(x)=4x+5 for x varying between -10 and 10 plot sin(x) for x between -pi/2 and pi/2 draw(4x+5,x,[-10,10]) plot sin(x) and cos(x) for x between -pi and pi draw x, x^2 and x^3 between 0 and 2 draw({sin(x), cos(x)}, x, [-pi,pi], [-2,2]) draw(1/x, x, [-5,5], [-10,10])
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Definitions

Functions, sequences and variables to reuse

define f=4x+8 and differentiate f if g(x) = x squared +5x then find the value for g(-2)+2 f(x) = 4*3^x calculate f(10) and f(1) evaluate |a+b|-c if a=2, b=-3 and c=-4 give the value of f(x)=cos(x/2) at 0 list the definitions clear the definitions
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Explanations

Understand why a calculation gives its result

explain 9-(-4) explain (-5)^2 explain -4*-4 explain -1/2*-4 explain 2x3x4/5 explain 4*8+9 explain 1/2+1/3 why is -x^4 equal to x^4 explain how -13-4 is -17 explain 3*4^2
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Miscellaneous

Decimals, scientific notation, word problems, checks

0.000123 * 2 in scientific notation calculate pi with 20 decimals What is the 32nd decimal of square root of 2 over square root of 3? if y varies inversely as x and y=4 when x=12, find y when x=2 show the help readme show that (x+1)^2-(x-1)^2=4x
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