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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate : $\int \frac{x^3}{x+2} d x$
  • A
    $\frac{x^3}{3}-x^2-4 x-8 \log |x+2|+C$
  • ✓
    $\frac{x^3}{3}-x^2+4 x-8 \log |x+2|+C$
  • C
    $\frac{x^3}{3}+x^2+4 x+8 \log |x+2|+C$
  • D
    $\frac{x^3}{3}+x^2+4 x-8 \log |x+2|+C$
✓

Answer

Correct option: B.
$\frac{x^3}{3}-x^2+4 x-8 \log |x+2|+C$
(b) : Let $I=\int \frac{x^3}{x+2} d x$
Dividing $x^3$ by $x+2$, we get
$
=\int\left(x^2-2 x+4-\frac{8}{x+2}\right) d x=\frac{x^3}{3}-x^2+4 x-8 \log |x+2|+C
$

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