Evaluate ∫ (x^3 - 1)/(x - 1) dx.

Question 12

MediumOriginal question

Evaluate $\int \frac{x^{3} - 1}{x - 1}\,dx$ .

\frac{x^{3}}{3} + \frac{x^{2}}{2} + x + C

Correct answerYour answer

x^{3} + x^{2} + x + C

Correct answerYour answer

\frac{x^{3}}{3} + \frac{x^{2}}{2} + C

Correct answerYour answer

\frac{x^{3}}{3} - \frac{x^{2}}{2} + x + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Divide first: $x^{3} - 1 = (x - 1)(x^{2} + x + 1)$ , so the integrand is $x^{2} + x + 1$ .
$\int (x^{2} + x + 1)\,dx = \frac{x^{3}}{3} + \frac{x^{2}}{2} + x + C$ .

Worth noting

$x^{3} + x^{2} + x$ raises each power but forgets to divide by the new power.

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