We have, y=∫√((x^3 1 3x^2+3x)x 1) dx y=∫√((x 1)^3x 1) dx y=∫√((x 1)^2) dx y=∫ (x 1) dx y=x^22 x+C Hence, this is the answer. ...

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Formation of Algebraic Expressions

y=∫√x3-1-3x2+...

Question

$y = \int \sqrt{\frac{(x^{3} - 1 - 3 x^{2} + 3 x)}{x - 1}} d x$

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Solution

We have,
$y = \int \sqrt{\frac{(x^{3} - 1 - 3 x^{2} + 3 x)}{x - 1}} d x$

$y = \int \sqrt{\frac{(x - 1)^{3}}{x - 1}} d x$

$y = \int \sqrt{(x - 1)^{2}} d x$

$y = \int (x - 1) d x$

$y = \frac{x^{2}}{2} - x + C$

Hence, this is the answer.

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