Question

Evaluate the function w.r.t.x $\int x^{2} (1-\frac{2}{x})^{2} \ dx$

Answer 1

this is the answer of This question

Answer 2

Answer:

$\dfrac {x^3 }{3} + 4x -{2x^2}+ C$

Step-by-step explanation:

We have to find the integration of ${x^2}(1- \dfrac 2x )^2dx$

First let us simplify the equation by the formula of $(a - b)^2 = a^2 +b^2 -2ab$

$x^2 (1 + \dfrac4x^2 - \dfrac 4x)$

$x^2 +4 - 4x$

Now,

$\int (x^2 + 4 -4x)dx$

$\int x^2 dx + 4\int dx - 4\int xdx\\ \dfrac {x^3 }{3} + 4x -\dfrac{4x^2} 2 + C\\\dfrac {x^3 }{3} + 4x -{2x^2}+ C$