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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int \frac{x^3-x^2+x-1}{x-1} d x$
  • ✓
    $\frac{x^3}{3}+x+C$
  • B
    $x^3+x+C$
  • C
    $\frac{x^3}{3}+x^2+C$
  • D
    $\frac{x^3}{3}+C$
✓

Answer

Correct option: A.
$\frac{x^3}{3}+x+C$
Let $ I=\int \frac{x^3-x^2+x-1}{x-1} d x$
$=\int \frac{x^2(x-1)+1(x-1)}{x-1}=\int \frac{\left(x^2+1\right)(x-1)}{x-1} d x$
$=\int\left(x^2+1\right) d x=\frac{1}{3} x^3+x+C$

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