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$\int\frac{x^3-1}{x-1}dx$
Learn how to solve integral calculus problems step by step online. Integrate the function (x^3-1)/(x-1). Find the integral. Rewrite the expression \frac{x^3-1}{x-1} inside the integral in factored form. Expand the integral \int\left(\frac{3}{4}+\left(x+\frac{1}{2}\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\left(x+\frac{1}{2}\right)^2dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+\frac{1}{2} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.