The hard integral thread.

there is a standard way of doing

(Acosx +Bsinx)/(Ccosx +Dsinx)

I know you can use a substitution to directly solve the integral however there is another nice way of doing it.

I haven't checked if the substitution works with a and b coefficients however it defiantly works for

$\displaystyle\int \dfrac{\cos{x}}{\sin{x} + \cos{x}} \mathrm{d} x$

I do not think you need substitution for any of these.

That is what I said, you can use a substitution although it doesn't have the beauty of the method I had in mind.

Could you elaborate on your method for me?

For AEAers or STEPers only
(just written and it is to be included into one of my papers)

I think x=9-2cosu shud work.


Posted from TSR Mobile

I know what works and as this will go to my IYGB Specials it requires no Further maths.
Maybe it works also
try it

Oh so you didn't use that sub? If not I'll try it now.


Posted from TSR Mobile

the sub is "special reserve" knowledge.
the answer is π - 2

the sub is "special reserve" knowledge.
the answer is π - 2

In the 2nd line I multiply top and bottom by (1-cosu)^1/2

Posted from TSR Mobile

the sub is "special reserve" knowledge.
the answer is π - 2

My method was this.

Substitution of $u^2 = x - 7$

By parts using $s = u$ and $\dfrac{\mathrm{d} t}{\mathrm{d} u} = \dfrac{u}{(4 - u^2)^{\frac{1}{2}}}$

Substitution of $u = 2 \sin{\theta}$


Granted its probably not the most elegant method.

In the 2nd line I multiply top and bottom by (1-cosu)^1/2

Posted from TSR Mobile

Those integral signs lmao.

Nice method. How did you spot that sub?

Those integral signs lmao.

Nice method. How did you spot that sub?

Not sure lol, i knew it would be some trig one. And just thought of the one that would work nicely to cancel something out.


Posted from TSR Mobile

Read carefully the comment in my solution and copy it into your "arsenal"
test it with another very easy one

If you wouldn't mind could you give me some advice? Do you have any tips on how to deal with exam anxiety, I tend to perform a lot worse when I'm under pressure and I'm scared that I will tank STEP despite putting in a lot of work this year. I know I'm not Zacken or anything but I really enjoy Maths, I want to prove to myself that I am good enough to get a good grade. I really don't want a repeat of MAT.

Read carefully the comment in my solution and copy it into your "arsenal"
test it with another very easy one