## ∫ [f(u) ± g(u)] du

### To integrate the expression ∫ [f(u) ± g(u)] du, you can apply the linearity property of integration

To integrate the expression ∫ [f(u) ± g(u)] du, you can apply the linearity property of integration. This property states that the integral of a sum or difference of functions equals the sum or difference of their integrals.

Therefore, you can rewrite the given expression as two separate integrals:

∫ f(u) du ± ∫ g(u) du

Now, let’s integrate each term individually:

∫ f(u) du:

To integrate f(u) with respect to u, you need to know the specific form of f(u). Different functions may require different integration techniques. In general, you can try to apply standard integration formulas or methods such as substitution, integration by parts, or trigonometric identities.

∫ g(u) du:

Similarly, you need to know the specific form of g(u) to integrate it. Apply the same integration techniques depending on the function.

After integrating each term, you can combine the results back together:

∫ [f(u) ± g(u)] du = ∫ f(u) du ± ∫ g(u) du

Note that the ± symbol implies that you choose either the plus or minus sign depending on whether you have a plus or minus sign between f(u) and g(u).

Make sure to check the simplification of the expressions or obtain the final answer if possible.

Remember that integration can often involve multiple steps and methods, so it’s important to have a clear understanding of the specific functions f(u) and g(u) that you are dealing with.

## More Answers:

The Sum Rule: A Fundamental Concept in Mathematics for Probability, Combinatorics, and AlgebraMastering the Difference Rule in Calculus: Derivatives of Functions Involving Subtraction

Mastering Integration Techniques: A Guide to Integrating Functions with the Constant Multiple Rule