Sorry, I should have asked more accurately.
I wanted to know why there is and not from
Do you differentiate part? I don't understand the meaning of
Since we know formula how can you get from ?
Shouldn't in this case equality be ? If that's the case, then where does disappear from and how gets from denominator to numerator?
Sorry, I must be a headache.
Just in case a picture helps...
Differentiate arcsin root x (travelling downwards)...
... where (key in spoiler) ...
Spoiler:
Then, working backwards through the chain rule to integrate the whole of the original fraction...
... where (key in spoiler) ...
Spoiler:
Spoiler:
Use the same diagram to check the integration by differentiating your result (i.e. by working down/clockwise instead of up/anti-clockwise through the same picture).
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
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