# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve calculus problems step by step online.

$u=x-1$

Learn how to solve calculus problems step by step online. Integrate int(x*(x-1)^3)dx with respect to x. We can solve the integral \int x\left(x-1\right)^3dx by applying integration by substitution method (also called U-Substitution). First, we must identify a part of the integral with a new variable, which when substituted makes the integral easier. We see that x-1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Rewriting x in terms of u. Substituting u, dx and x in the integral and simplify.

$\frac{\left(x-1\right)^{5}}{5}+\frac{\left(x-1\right)^{4}}{4}+C_0$

### Problem Analysis

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

Calculus

~ 0.09 seconds