# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\left(x-\frac{1}{3}\right)^3dx$

Learn how to solve calculus problems step by step online.

$\begin{matrix}u=x-\frac{1}{3} \\ du=dx\end{matrix}$

Learn how to solve calculus problems step by step online. Calculate the integral of int((x-1*(1/3))^3)dx. Solve the integral \int\left(x-\frac{1}{3}\right)^3dx applying u-substitution. Let u and du be. Substituting u and dx in the integral and simplify. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a constant function. Substitute u back for it's value, x-\frac{1}{3}.

$\frac{\left(x-\frac{1}{3}\right)^{4}}{4}+C_0$

### Problem Analysis

$\int\left(x-\frac{1}{3}\right)^3dx$

Calculus

~ 0.03 seconds