How to Use the Power Rule in Calculus

Apply the rule of power or rule of integration can help us solve various mathematical problems. If you are looking to understand how the rule of power works, you will be glad to know that you have come to the right place. The rule of integration can give you a generalised solution to a problem containing any variable raised to any power except minus one. A variable containing a power -1 is considered a special case in mathematics. Considering the fact integration is the derivative of function, solving the problems gives the original function.

Things Required:

– Paper
– Pencil


  • 1

    Before doing anything else you will need to make sure that you have some basic algebraic knowledge. Without knowing the terms used in the rule of power, you will not be able to solve the problem effectively and efficiently. Consider converting any square roots and roots of other powers in the given equation. Convert powers in denominators to standard power functions to come up with the solution to a problem. Make sure you familiarise yourself with the functions given below prior to applying the rule of integration.

    - The square root of x equals x^(1/2)
    - The cube root of x equals x^(1/3)
    - and so on for the other roots.

  • 2

    It is recommended to take the inverse of the power: 1/x^2 = x^-2, for example to be able to solve a power from denominator to the numerator. Next, add one to the power of the variable for which you are looking to solve the equation.

  • 3

    For int[(x^5)dx], for example, x^4 becomes x^5. Now consider diving the result by the new power, which will be:

    x^4 gives (x^4)/4.

  • 4

    You must use the constant of integration when converting denominator into numerator. Constant of integration is represented by c and this must be used to get accurate results. For example, c must be added to [(x^4)/4] for the above example.

  • 5

    Integrating a constant is also very simple. Just think of the constant as being a variable with zero power. It is advised to solve each part of the function separately if you are looking to solve an equation with subtraction or addition functions. Remember to take your time and follow the steps. If you have any issues then start the instructions again and try not to skip the steps. You can also ask someone who has more mathematical knowledge then yourself for some assistance.

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