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it said use t=tan(x/2), but its a coroneos question, and i'd doubt it'd be in an exam, Anyways, can someone please help me on this t-formula integration which involves trigonometric squares? Q. INT (sinx^2)/(1+cosx) dx I did it and ended up with having to integrate (2t^2)/(1+t^2)^2 Did I do...

t=tanx worked normally, but the question specified t=tan(x/2) When I tried it, I used the double angle formula while resulted in a (cosx)^2 being in the expression, which resulted in ((1-t^2)/(1+t^2))^2 --. ugly and complicated stuff anyone know if theres a quick easy way to use tan(x/2) = t...

Hey guys, just wondering is there any way that you can use: t=tan(x/2) in order to simply/easily integrate 1/(1+3cos2x)? Or is it advisable to use t=tanx? Thanks

Thank you... the piece of gold I was searching for...

I know, I know, but partial fractions would take up an extra minute in an exam, and every second counts in a 4U exam...

lol all you have to do is state what the formula is... :) Thanks anyways :)

Hi guys, quick question: I know the formula for integrating 1/(x^2 - a^2) = (1/2a)[ln(x-a) - ln(x+a)] + c and for integrating 1/(a^2 - x^2) = (1/2a)[ln(a+x) - ln(a-x)] + c --- So I was wondering, what is the formula for e.g. integrating 1/(a^2 - [f(x)]^2)?? Vice versa, formula for...

ahh i see now thanks man

Hi guys, I'm having confusion over one particular thing, a lot of my integration questions, part of the answer is in the form of e.g. ln(3-4x), whereas my answer was ln(4x-3). e.g this question from Coroneos: integrate 1/(16-9x^2) what I did was factor out the 1/(-9) so it I would have to...

ahh i see thanks

Ok, thankyou for the advice for the 1st question, I seem to have gotten the answer As for the 2nd one, I know you said it is hard to explain... but is it something to do with partial fractions..? What method exactly would be used here? Thanks

Hi, can't seem to do these two questions: Q1. integrate sqrt[(1+x)/(3+x)] Q2. integrate (cosx + 3sinx)/(3cosx + 4sinx) Help is greatly appreciated

Can someone provide a solution on how to solve (4x^2 + 1)/((x-2)(x+2)^3)? I can't seem to do it Thank you

Hi, I'm still coming to terms with the idea of integration by partial fractions, and there are a few questions types that I am having trouble with: Q1. Integrate (4x^2 +1)/[(x-2)(x+2)^3] So how do I split it? Do i do this? -- A/(x-2) + B/(x+2) + C/(x+2)^2 + D/(x+2)^3 or do i do this --...

Hi, here's another question that I am having a lot of trouble with; Q. integrate 1/(x^3 -1) I used the partial fractions method, which led me to integrate the following expression: 1/[3(x-1)] - (x+2)/[3(x^2 + x +1)] dx Now I know how to integrate 1/3(x-1)... but HOW do i...

matee.... pretty sure tan^2 x +1 = sec^2 x not tan^2 x -1 = sec^2 x

Are there alternative methods/substitutions?

Thankyou for the prompt reply. But if you were to do these questions, would you follow the same methods/substitution I used, or do you see a different more approachable way?

Hi, I'm having trouble with a few questions: Q1. integrate: (sec^2 x)/(tan^2 x -1) so I let u=tanx, and ended up having to integrate 1/(u^2 -1). How do I integrate this? The table of standard integrals doesn't specify a particular way to integrate this, so could some please shed some light...

aahh i see thanks trebla, and yeah i did get ln(1+root2)