Find the integral- -x3-x2-x-1 x-1 dx

∫x^3 x^2+x 1 x 1 dx nbsp; = ∫x^2 (x 1) +(x 1) x 1 dx =∫(x^2 + 1) (x 1) x 1 dx = ∫ (x^2 + 1) dx =∫ x^2 nbsp; dx + nbsp;∫ dx nbsp; nbsp; = nbsp; ( x^2+1 ...

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Standard XII

Mathematics

Binomial Integral

Find the inte...

Question

Find the integral: $\int \frac{x^{3} - x^{2} + x - 1}{x - 1} d x$

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Solution

$\int \frac{x^{3} - x^{2} + x - 1}{x - 1} d x$
$= \int \frac{x^{2} (x - 1) + (x - 1)}{x - 1} d x$
$= \int \frac{(x^{2} + 1) (x - 1)}{x - 1} d x$
$= \int (x^{2} + 1) d x$
$= \int x^{2} d x + \int d x$
$= (\frac{x^{2 + 1}}{2 + 1}) + x + C$
$= \frac{x^{3}}{3} + x + C$
Where $C$ is constant of integration

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Binomial Integral

Standard XII Mathematics

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Find the integral: ∫x3−x2+x−1x−1dx

∫x3−x2+x−1x−1dx =∫x2(x−1)+(x−1)x−1dx =∫(x2+1)(x−1)x−1dx =∫(x2+1)dx =∫x2dx+∫dx =(x2+12+1)+x+C =x33+x+C Where C is constant of integration

Find the integral: $\int \frac{x^{3} - x^{2} + x - 1}{x - 1} d x$