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# Integration of algebraic fractions Watch

1. I thought that I would be best served by splitting the fraction into two. Therefore, I had 1/x^2; which I identified as being equal to x^-2. Adding one to that; simplified that, and I got -1/x

The second part of my "solution" was -x^3/x^2. I thought that because there was indices and division involved, this meant that I would subtract the indices from one another, leaving me with -x^1. Adding one to that gave me -x^2.

However; the online integral calculator has listed the result as -x^2/2
2. The x terms can be simplified.

The 1 obviously turns into an x. You should be sorted.

If all divided by x^2 then.... Integral of 1/x^2 - x after you've simplified the x terms. Then 1/x^2 = x^-2.... so Integral of x^-2 - x then integrate and add +c
3. (Original post by apronedsamurai)
Is all of the 1-x^3 divided by the x^2

If so

(1-x^3)/x^2 = 1/x^2 - x

1/x^2 is the same as x^(-2)

So

Once again

Increase the power and divide
4. What IS the proper form for -x^2?

I had thought it was - 1/x^2
5. (Original post by apronedsamurai)
What IS the proper form for -x^2?

I had thought it was - 1/x^2
Is this a different question
6. No,

I am trying to narrow down where I have went wrong.
7. (Original post by apronedsamurai)
No,

I am trying to narrow down where I have went wrong.
Well this question does not include -x^2

1/(x^2) = x^(-2)
8. (Original post by apronedsamurai)

I thought that I would be best served by splitting the fraction into two. Therefore, I had 1/x^2; which I identified as being equal to x^-2. Adding one to that; simplified that, and I got -1/x

The second part of my "solution" was -x^3/x^2. I thought that because there was indices and division involved, this meant that I would subtract the indices from one another, leaving me with -x^1. Adding one to that gave me -x^2.

However; the online integral calculator has listed the result as -x^2/2
The integral of -x is indeed

You seem to have forgotten the basic rule about dividing by the new power when you integrate something of the form - you get

The way to check these things is ALWAYS to differentiate your final answer and check that you get back the original function.

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Updated: January 17, 2015
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