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Find the integral $\int x^2(1-\frac{1}{x^2})\;dx$

1 Answer

Solution: $\frac{1}{3}x^3-x+k$

Toolbox:

$\int $$x^n$ $=$ $\frac{1}{n+1}$ $x^{n+1}$. 

Step 1:

$x^2(1 - \frac{1}{x^2}) = x^2 - \frac{x^2}{x^2} = x^2 - 1$

Step 2:

$\int x^{2} dx = \frac{1}{2+1} x^{2+1} = \frac{1}{3} x^3$

Step 3:

$\int dx = x$

Step 4:

Solution = $\frac{1}{3}x^3 - x + k$

 

answered Dec 6, 2012 by balaji.thirumalai
 
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