Integrate (x-11/3)^3

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

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Answer

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

Step by step solution

Problem

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

Multiply $-1$ times $\frac{1}{3}$

$\int\left(x-\frac{1}{3}\right)^3dx$
2

Solve the integral $\int\left(x-\frac{1}{3}\right)^3dx$ applying u-substitution. Let $u$ and $du$ be

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

Substituting $u$ and $dx$ in the integral

$\int u^3du$
4

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$\frac{u^{4}}{4}$
5

Substitute $u$ back for it's value, $x-\frac{1}{3}$

$\frac{\left(x-\frac{1}{3}\right)^{4}}{4}$
6

Add the constant of integration

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

Answer

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

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Problem Analysis

Main topic:

Integration by substitution

Time to solve it:

0.22 seconds

Views:

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