Integrating 1/x^3: -2/x^2 or -1/2x^2?

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SUMMARY

The integration of the function 1/x^3 results in -1/2x^2. The process involves rewriting 1/x^3 as x^-3, then integrating to obtain x^-2/-2. The correct conversion back to fractional form confirms that the result is -1/2x^2, not -2/x^2. This conclusion is definitive based on the rules of integration for power functions.

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Hi,

ive got a really simple question, but I am just slightly confused,
im trying to integrate 1/x^3 , now i take x^3 to the top and i get x^-3, and now when i intergrate that i get:

x^-2/-2 (i think)
now when i put it back into fractional form do i get:

-2/x^2 or -1/2x^2 ?
 
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(x^-2)/-2 = -1/(2x^2)
 


Thanks for your question! The correct answer is -1/2x^2. This is because when you integrate x^-3, you bring the power up by 1 to get x^-2 and then divide by the new exponent, which is -2. This results in -1/2x^2. Hope this helps!
 

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