(January 15, 2014 Update: Step-by-step solutions has been updated! Learn more.)
Have you ever given up working on a math problem because you couldn’t figure out the next step? Wolfram|Alpha can guide you step by step through the process of solving many mathematical problems, from solving a simple quadratic equation to taking the integral of a complex function.
As you can see, Wolfram|Alpha can find the roots of quadratic equations. Wolfram|Alpha shows how to solve this equation by completing the square and then solving for x. Of course, there are other ways to solve this problem!
Wolfram|Alpha can demonstrate step-by-step solutions over a wide range of problems. This functionality will be expanded to include steps for solutions in other mathematical areas. Look through the following examples to see the abilities of the “Show steps” functionality.
If you need to learn how to do long division of polynomials, Wolfram|Alpha can show you the steps. Let’s try (x5–14x4+3x2–2x+17)/(2x2–x+1):
If you are stumped trying to find the limit of xx as x->0, consult Wolfram|Alpha:
When you need to find the derivative of (3x2+1)/(6x3+4x) for your calculus class, Wolfram|Alpha will find this derivative using the quotient rule.
Are you trying to integrate e2 x cos(3x), but forgot the formula for integration by parts? Wolfram|Alpha will remind you how to integrate by parts.
Wolfram|Alpha can do virtually any integral that can be done by hand. Try the integral of x?[1–?[x]]:
Wolfram|Alpha also has the step-by-step functionality for partial fractions. Try partial fractions of 1/(x3–1):
The step-by-step programs in Wolfram|Alpha rely on a combination of basic algorithms and heuristics including Gaussian elimination, l’Hôpital’s rule, and Bernoulli’s algorithm for rational integration. These heuristics are a logical formulation of the natural methods used by humans for solving problems. By utilizing Mathematica’s powerful pattern-matching capabilities, Wolfram|Alpha’s developers have morphed these rules into a platform for breaking down and structuring the solutions to complicated problems, which closely mimics the ways by which a human would solve problems of these natures.
The “Show steps” feature allows you to learn basic mathematics on your own, or it can simply be a nice way to check your work! It can also give you insight on different ways to solve problems. So next time you find yourself ready to give up on a math problem, make sure to check with Wolfram|Alpha. Visit the Wolfram|Alpha Homework Day Gallery for examples of how you can use Wolfram|Alpha as a learning tool for other subjects.