Integration : f'(x)/f(x) types leading to ln|f(x)| : ExamSolutions

Tutorial on how to integrate when the differential of a function is divided by the function.

[batmani]

It's unbelievable how well you explain things, been watching almost all your videos for about 3 months now, got every single Maths A level exam coming up in May June, I WILL be ready for it.

[johnvannewhouse]

DAMN!! Just a GREAT video. I have MASSIVE issue with ln and e and these videos have made it SO SIMPLE to understand what is going. I actually - dare I say it? - feel comfortable with the processes of integration after watching these tutorials. Why the hell didn't our teachers or TA's show us this?!?!!?

[brianevans]

I'm in university now, and I'm still watching your videos. You are so good at explaining integration and calculus methods in general!

[Anas-nuio]

ur videos r gr8. I could learn A level maths in 2 days using ur videos. thanks soo much.

[tobydunbar]

Thank you so much!!!! You're an excellent teacher!!!!

[ExamSolutions_Maths]

I would suggest going through the videos sequentially.

[ExamSolutions_Maths]

Have you tried differentiating ln(4x-3) that may answer your question.

[lhaaale]

Really cleared this up for me - thank you!

[HazzzProductions]

No, because if you differentiate that you need the product rule and you would get something totally different. You can only pull out constants from the differentiation. cos^2x is a variable.

[jiyapatel]

So helpful! really appreciate your work 😊

[Finalizable]

where can I find the video talking about why intergration 1/x gives ln mod x not just lnx thanks

[forpersonaluseonly]

@Bayzid Tanx=sinx/cosx. As Cotx=1/tanx it also equals 1/sinx/cosx which is cosx/sinx (flip fraction) Hope this helped you! :)

[ExamSolutions_Maths]

yes, ln(x-3)(x+2) + c = ln(x^2-x-6) + c

[TSMK]

So for question 4, you are allowed to move the constant 2 in the denominator and change the constant 8 of the numerator into a 4?

Is this law allowed only in the case where you want the differential of the numerator to become a differential of the denominator?

Please help me.

[goshtin]

what kind of fractions does this NOT work on? how can you tell the difference?
and do you have a vid for integrating fractions otherwise?
thanks

[sholaameobi]

In question 6, I subbed 1/tanx in for cotx and ended up with cos^2x.ln|tanx| + C

Obviously more complicated, but is it still right?

[alvinlepik]

a technical question - is it necessary to put the function of ln - say ln (x² + a) - into mod signs when it s seen immediately that it will always be > 0
. And should a and x be 0, then we would have to take a log of 0. Should it be pointed out if in ln [f(x)]  the function could be 0 and hence give a range in which the calculation is possible?

[raheelmahmood]

In question 4 you pulled out 2 as a constant and were left with 4x inside. In question 5, why did u pull out 1/2 instead of 2? Wouldnt it be 2(x+3) and then you write the constant 2 outside? Thats what i was expecting to happen but now im very confused

[shathiswaryroysaravanan]

Can I know y should I put that X in a modulus like lxl?

[muhaimen]

On your second example why does the 4 disappear when you integrate?