Thanks! Couldn't wait till Saturday to find out :P
How do you even come up with these questions?
those two are dead easy to make.
think of a disgusting function differentiate it then give to students to reverse the order, i.e. integrate
Today I am off and I made 2 very hard integrals, for the mathematicians only, i.e no clues and I am currently working on a third but it is giving me trouble for the last 2 hours
think of a disgusting function differentiate it then give to students to reverse the order, i.e. integrate
Today I am off and I made 2 very hard integrals, for the mathematicians only, i.e no clues and I am currently working on a third but it is giving me trouble for the last 2 hours
These are really neat when using the substitution though, surely that requires some more thinking?
Are those integrals solve-able using A level maths knowledge? If so please share
sorry but it is not correct. There is no ln(...) in this one final answer is very simple
do you need a hint?
I used u = rootx as a substitution to get:
2*integral(1 + (1/(u^2 + 1)) - (2/((u^2 + 1)^2)) du
and then to integrate that I substituted x back in (so multiplied it all by 1/(2rootx) since du = dx/2rootx), split all that into partial fractions and integrated
does that seem like a correct method? I'm pretty sure I made a mistake in the partial fractions bit since I ran out of paper and had to squeeze it all into the bottom of a page
If there's something wrong with this method then may I please have the hint
2*integral(1 + (1/(u^2 + 1)) - (2/((u^2 + 1)^2)) du
and then to integrate that I substituted x back in (so multiplied it all by 1/(2rootx) since du = dx/2rootx), split all that into partial fractions and integrated
does that seem like a correct method? I'm pretty sure I made a mistake in the partial fractions bit since I ran out of paper and had to squeeze it all into the bottom of a page
If there's something wrong with this method then may I please have the hint
The standard way is
u=rootx then you get partial fractions which are improper, repeated and irreducible!!!!!! This is very easy to go wrong Then you will need to know how to integrate back into an arctan and then you are done....
Once you achieve the solution in this way then you can see what substitution would clear this mess quicker
u=rootx then you get partial fractions which are improper, repeated and irreducible!!!!!! This is very easy to go wrong Then you will need to know how to integrate back into an arctan and then you are done....
Once you achieve the solution in this way then you can see what substitution would clear this mess quicker
Thanks! Did I get the first bit right then (the partial fractions in terms of u)? What do you mean integrate back into an arctan?