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Home  >>  CBSE XII  >>  Math  >>  Integrals
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Find the integral $ \LARGE {\int } \normalsize \frac{\large x^3-x^2+x-1}{\large x-1}\;dx$

$\begin{array}{1 1} (A)\; \large\frac{x^3}{3}+x+c \\(B)\; \large\frac{x^3}{3}-x+c \\(C)\; \large\frac{x^2}{3}+x+c \\ (D)\; \large\frac{x^3}{3}+2x+c\end{array} $

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1 Answer

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Toolbox:
  • $\large\frac{d}{dx}$$(x^n)=nx^{n-1}$
Given : $\int \large\frac{x^3-x^2+x-1}{(x-1)}$$dx$
Factorize the Numerator :-
$\int \large\frac{x^2(x-1)+1(x-1)}{(x-1)}= \int \large\frac{(x^2+1)(x-1)}{(x-1)}$
$\qquad\qquad\qquad\quad=\int (x^2+1)dx$
$\qquad\qquad\qquad\quad= \large\frac{x^3}{3}$$+x+c$
answered Sep 10, 2013 by sreemathi.v
 
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