Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int \frac{x^3-x^2+x-1}{x-1} d x$
A
$\frac{x^3}{3}+x+C$
B
$x^3+x+C$
C
$\frac{x^3}{3}+x^2+C$
D
$\frac{x^3}{3}+C$
✓
Answer
$\begin{array}{l}\text { (a) : Let } I=\int \frac{x^3-x^2+x-1}{x-1} d x \\ =\int \frac{x^2(x-1)+1(x-1)}{x-1}=\int \frac{\left(x^2+1\right)(x-1)}{x-1} d x \\ =\int\left(x^2+1\right) d x=\frac{1}{3} x^3+x+C\end{array}$
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