$\int \frac{(x^{3} + 3) (x - 2)}{(x^{2} - 4 x + 4)} d x$

Open in App

Solution

We have,
$I = \int \frac{(x^{3} + 3) (x - 2)}{(x^{2} - 4 x + 4)} d x$

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

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

$I = \int (x^{2} + 2 x + 4 + \frac{11}{x - 2}) d x$

$I = \frac{x^{3}}{3} + 2 \frac{x^{2}}{2} + 4 x + 11 ln (x - 2) + C$

$I = \frac{x^{3}}{3} + x^{2} + 4 x + 11 ln (x - 2) + C$

Hence, this is the answer.

Suggest Corrections

Similar questions

x^{3} + 5 x^{2} + 4 x - 4

x^{2} + 3 x - 2

(x^{3} - 3 x + 2)

(x^{2} - 4 x + 3)

Integrate the rational functions.
$\int \frac{(x^{2} + 1) (x^{2} + 2)}{(x^{3} + 3) (x^{2} + 4)} d x$

\int \frac{(x^{3} + 8) (x - 1)}{x^{2} - 2 x + 4} d x

Join BYJU'S Learning Program