csc2iffy said:Homework Statement
[itex]\int[/itex](x^(1/3)/(x^(1/3)+1))dxHomework Equations
I know I have to use u substitution
u=x^(1/3)
du=1/(3x^(2/3))dxThe Attempt at a Solution
I know that the denominator of the equation will be u+1, but I don't understand how to find the numerator because I thought it would just be u, but wolfram alpha says it's u^3?
An indefinite integral is the inverse operation of differentiation and is used to find the original function when given its derivative. It is represented by the integral symbol (∫) and is accompanied by a variable of integration.
The process for finding an indefinite integral involves using integration techniques such as substitution, integration by parts, or trigonometric substitution. The resulting integral will be a function with a "+ C" at the end, representing the constant of integration.
An indefinite integral represents a family of functions while a definite integral represents a specific value. In other words, an indefinite integral gives a general solution while a definite integral gives a specific answer.
One way to check if you have found the correct indefinite integral is by differentiating the result. If the derivative is equal to the original function, then the indefinite integral is correct. Additionally, you can use integration tables or online calculators to verify your answer.
Finding indefinite integrals is used in various fields such as physics, economics, and engineering. For example, it can be used to calculate the displacement of an object over time, determine the total cost of goods sold, or find the area under a curve in a force vs. distance graph.