Wolfram|Alpha

Step-by-Step Solutions

Physics Formulas

do physics calculations step by step
work W=30J, d=100m photon energy 435nm

Chemical Structures

get a step-by-step procedure to draw the Lewis structures of molecules
What is the Lewis structure of NO2 Lewis dot structure of ATP

Chemical Conversions and Properties

follow the steps for unit conversion
convert 5mL benzene to moles how many molecules are in 10 grams of ATP
compute oxidation states of chemicals
oxidation states of chromium(III) chloride elemental oxidation state of copper(II) sulfate

Chemical Reactions

learn how to balance a chemical reaction
glucose + oxygen -> water + carbon dioxide Cu + HNO3 -> Cu(NO3)2 + NO2 + H2O
calculate reaction stoichiometry
0.2 mol CH4 + O2 -> 7 mL H2O + CO2 benzene + nitronium (ion) -> 0.02 mols nitrobenzene + hydrogen (ion)

Arithmetic

check your work using step-by-step arithmetic
60431 / 89 9 (3+1) + 17 / (6-12)
follow the steps to convert an improper fraction to a mixed number
87/5 as a mixed number

Number Theory

find step-by-step solutions for prime factorization, primality testing, GCD, and more
is 73 prime? lcm(90, 342) are 12 and 21 coprime?

Statistics

perform basic statistical analysis on a set of data, seeing the steps along the way
average of {1, 2, 3, 4, 5, 6, 7} mode of {1, 5, 4, 2, 3, 4, 5, 11, 4, 11, 20} variance 4, 6, 7, 9, 10, 11 quartile of {1, 2, 3, 4, 5, 6}

Intercepts

find axis intercepts one step at a time
x intercepts of sin(x) y intercept of x^2+1 intercepts of (x^2+2)(x^2-1)

Trigonometry

see the steps toward proving a trigonometric identity
(1 + tan(x))/(1 – tan(x)) = (cos(x) + sin(x))/(cos(x) – sin(x)) cot(t/2)^2 = (1 + cos(t)) / (1 – cos(t))

Algebra

evaluate an expression at a point one step at a time
evaluate x^2 + 2(x + 7) - 19 at x = 7 (x - 1)(x + 3)^2 + 7 where x = 2
solve equations one step at a time
x^2 + 5x + 6 = 0 solve (9^(x + 1)) – (28 (3^(x))) + 3 = 0 over the real numbers
factor polynomials step by step
factor x^4+4 factor x^3+2x^2+x+2
expand polynomials using FOIL, the binomial theorem, and other methods
expanded form of (x + 3)^2 multiply out (x^2 + x)^4
choose from multiple methods to complete the square
complete the square x^2 + 2x + 3 complete the square x^2 + y^2 + 2x + 4y - 11 = 0
simplify rational expressions with steps provided
simplify (1/a + 1/b) (a + b) k/(k + 1) + 1/((k + 1) (k + 2))
learn to rewrite a rational function using our step-by-step partial fraction decomposition
partial fraction decomposition 1/(x^2 + 4x + 3) 1/(x^3 + 4x^2 + 5x + 2)

Calculus

find the derivative using the product rule, chain rule, and other methods
derivative of x^4 + 9x^3 + 7x – 2 slope of log(x) / (x^2 + 1)
calculate an integral by substitution, integration by parts, and other methods
integrate sin(x)cos(x)^2 integral of sqrt(a^2 – x^2) show the integration: arcsec(sqrt(t))
learn how to take a limit
limit of (x – 3) / (x^2 – 2x – 3) as x approaches 3 take the limit as x goes to infinity: (1 + 1/x)^x
find local and global extrema using a variety of tests
local extrema of x^3 - 3x + 1 find the extrema of 3x^4 - 4x^3 - 12x^2 + 1 maximize sin(x)

Discontinuities

get hints for discontinuities
where is (x^2 - 4)/(x^2 - 2x - 3) discontinuous? discontinuities of sin((x^2-x)/(x-1)) + log(sqrt(abs(x)))

Differential Equations

see how ordinary differential equations are solved
y‘(t) – 2y(t) = 3 e^(2t) t^2 y‘(t) + 2t y(t) = t^4 y(t)^2 + 4 y''+ y = sin(2x)

Linear Algebra

write a matrix in reduced row echelon form one step at a time
{{1,1,5},{1,-1,1}} row reduce reduced row echelon form: {{1, -3, 3, -4}, {2, 3, -1, 15}, {4, -3, -1, 19}}
find the determinant step by step with various methods
determinant of {{1,2}, {-1, 2}} determinant of {{1,2,1}, {1,1,0}, {0,1,1}}
invert a matrix one step at a time
inverse {{1, 1, 2}, {-1, 2, 2}, {3, 2, 3}}
compute a cross product step by step
(1,2,3)x(3,4,5)
compute eigenvalues and eigenvectors step by step
eigenvalues {{3,-1},{0,2}} eigenvectors {{7,0,-3},{-9,-2,3},{18,0,-8}}

Mathematical Induction

prove a sum identity by induction
prove by induction sum of j from 1 to n = n(n+1)/2 for n>0
prove divisibility by induction
using induction, prove 9^n-1 is divisible by 4 assuming n>0
prove an inequality by induction
prove by induction (3n)! > 3^n (n!)^3 for n>0