wow thats amazing, I would never have thought of doing that in the exam ! thanks so much.
Out of curiosity, are there any clear things to look for , so you know which integration technique to use ? from partial, sub and by parts ?
The thing is, here - long division and substitution would have worked as well as just this basic simplification. You might want to learn "long division for polynomials" so you're able to do what I did in my previous post but without it requiring any creative thought and it's a lot more systematic.
You tend to get used to what technique to use once you've done enough practice; normally IBP is when you have a product of two functions where each is easy integrable/differentiable but put together they aren't, etc...
The thing is, here - long division and substitution would have worked as well as just this basic simplification. You might want to learn "long division for polynomials" so you're able to do what I did in my previous post but without it requiring any creative thought and it's a lot more systematic.
You tend to get used to what technique to use once you've done enough practice; normally IBP is when you have a product of two functions where each is easy integrable/differentiable but put together they aren't, etc...
What about partial fractions ? Could we have used partial fractions for the above question ?
What about partial fractions ? Could we have used partial fractions for the above question ?
Well, no - you can only use partial fractions when there is more than one factor in the denominator. But all you have here is (1+x) in the denominator, which you can't do anything with, unfortunately.
Well, no - you can only use partial fractions when there is more than one factor in the denominator. But all you have here is (1+x) in the denominator, which you can't do anything with, unfortunately.
what about e^ root(x) / root(x)
My textbook does it by Integration by substitution, but the fact is has two terms, suggested to me it should be Integration by parts ?
Is this a legitimate maths rearranging technique http://i.imgur.com/i1kWglN.jpg ie multpiply numerator and denominator by 2
Very much so! You learnt about this technique in middle school, I'm sure. How do you add 21+41. Well, you take the 21 and multiplied the numerator and denominator by 2 to get 42. So that you could write 21+41=42+41=43.
So, to answer your question, yes: what you've done is valid.