Question: \begin{align} \int \frac{x^3 - x^2 + x - 1}{x-1} . dx\end{align}

Answer:

\begin{align} \int \frac{x^3 - x^2 + x - 1}{x-1} . dx\end{align}

On dividing, we obtain

\begin{align} =\int \left({x^2 + 1}\right) . dx \end{align}

\begin{align} =\int {x^2} . dx + \int 1 .dx \end{align}

\begin{align} =\frac {x^3}{3} + x + C \end{align}

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Question: \begin{align} \int \frac{x^3 - x^2 + x - 1}{x-1} . dx\end{align}

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