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

[angel]

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 ?

 

[Inspector Gadget]

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

 

[M98Ranger]

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!