Complete the table to find the indefinite integral. Original Integral Rewrite Integ

step 1 Okay, so for this problem, we're going to carry it a three -step process. First, going to rewrit

Complete the table to find the indefinite integral. ...

Complete the table to find the indefinite integral.
$$\begin{array}{lll}\text { Original Integral } & \text { Rewrite } & \text { Integrate } & \text { Simplify } \\ \int \frac{1}{(3 x)^{2}} d x & \text { ______ } & \text { ______ } & \text { ______ } \end{array}$$

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Key Concepts

Power Rule for Integration

The power rule is a fundamental technique for integrating expressions of the form x^n. It states that the integral of x^n with respect to x is x^(n+1)/(n+1) plus a constant, as long as n is not equal to -1. This rule is essential when dealing with functions that are expressed as powers of x after algebraic manipulation.

Handling Constants in Integration

When integrating, constants can be factored outside of the integral sign due to the linearity of integration. This process simplifies the integral by reducing it to the integration of a simpler function, and requires careful manipulation of multiplicative constants during both the rewriting and integration stages.

Algebraic Manipulation in Integration

This concept involves rewriting the integrand into a simpler or more standard form that is easier to integrate. It often requires expressing expressions by factoring constants or rewriting exponents to reveal patterns compatible with standard integration rules.

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