integration help ! (1 Viewer)

natnat96

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heyyy if anyone is bored and wants to help !

∫x^3/(2x+1) dx

i tried dividing the thing first but i didnt get the right answer :/
 

Sy123

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heyyy if anyone is bored and wants to help !

∫x^3/(2x+1) dx

i tried dividing the thing first but i didnt get the right answer :/


By doing long division, we can see that:





 

natnat96

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ohhh jokes my long division was wrong and this is a definite integral in my textbook. i had a 2 instead of a 4 nek minut...hahahah
thanks guys !!
 
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If you are uncomfortable with long division, you can try this method:

We know that a power 3 divided by power 1 will result in a power 2 polynomial with a remainder (some constant).

We can write the quotient tentatively as:



It is a good alternative to lengthy and sometimes troublesome long divisions.
 
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Capt Rifle

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If you are uncomfortable with long division, you can try this method:

We know that a power 3 divided by power 1 will result in a power 2 polynomial with a remainder (some constant).

We can write the quotient tentatively as:



It is a good alternative to lengthy and sometimes troublesome long divisions.
That's a smart alternative actually....
 
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It seems so lengthy though...

How about this:












Essentially long division without the long division.
That's great if you are good at spotting what coefficients to put in and balance. If you are completely lost starting from scratch (with constants to find) is perhaps a more 'direct' route, rather than fumbling around with constants (esp in exams).
 

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