How to know the difference between... (1 Viewer)

1722

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okay so this is probably the stupidest question ever but:

How do you know if the derivative you are integrating will be a log/exponential function or a err simple function (if the derivative is in the form of a fraction)?
For example if it tells you to integrate:

x2/x3+7

or

x2-2x2+3/3x5

How do you know which one will integrate into a log/exponential or just a regular function?
 

SharkeyBoy

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look at the powers. if the denominator has a higher power of one more than the numerator, then it integrates to a log.
is that what you're asking?
 

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Yes omg! Thank you! It's been bothering me for ages and I couldn't find where the difference was! Thank you sooo much! :)
P.S Nobody taught me when I was learning it in school
 

bedpotato

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It's not always the powers.

When you differentiate ln(f(x)), the derivative is f'(x)/f(x)
So if you integrate f'(x)/f(x), wouldn't it be ln(f(x)) since integration is the reverse of differentiation.

The same rule applies when inegrating functions such as x^2/x^3 + 7, where f(x) is x^3 + 7 and f'(x) is x^2

E.g. If the question asks you to integrate cosx/sinx, you can't look at the powers.

Instead, differentiate the denominator, d/dx(sinx) = cosx
If the derivative of the numerator is the same as the numerator, use log.
 

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