I think you need uni level maths to do that.I'm afraid I have to step in here.
What is 1+1
with the s sub why when differentiated sin is negative cosLet
Let
Ill save the partial fractions working.
Drawing up a triangle we find:
So:
I could have very easily made a mistake whether in latex or just trying to evaluate to integral so let me know if you find any
Pretend you didnt see that . Also yes rookie mistake and fixed.with the s sub why when differentiated sin is negative cos
It's ok it's amazing you even were able to get to that point. I saw another one but I think I may be wrong because you and vern got to the same point but also the first sub why is the differential of tan -sec squaredPretend you didnt see that . Also yes rookie mistake and fixed.
Yeah honestly don't know what I was thinking, ironically the final answer is correct since the two negatives (which were both mistakes) cancel out.It's ok it's amazing you even were able to get to that point. I saw another one but I think I may be wrong because you and vern got to the same point but also the first sub why is the differential of tan -sec squared
Dw you fixed it
Yeah everything is good till the last step when you have to convert the u to a w so you will get a square root again.Something's very wrong, I can feel it.
You're invincible at maths. Even when you make mistakes it's not really a mistake and works out in your favor.Yeah honestly don't know what I was thinking, ironically the final answer is correct since the two negatives (which were both mistakes) cancel out.
i just gave up at the end cuz i knew it was gonna look uglyYeah everything is good till the last step when you have to convert the u to a w so you will get a square root again.
Yep and you would have got what Vern and I got. The sub does your two subs in one.i just gave up at the end cuz i knew it was gonna look ugly
actually i couldve subbed in w = tanv or something
After looking at my working I found a big brain substitution:Just a question. The standard way to do this integral seems to look like a page of working at least.
Any short ways?
Finding the antiderivative is very easy using a t-sub. I've shown a different way the antiderivative can be found below:It's not too hard to get the antiderivative in terms of elementary function...but the evil is in the substitution of upper and lower limits.
Ok, thanks for the insight!Periodicity is not the cause of this trouble. If you integrate cos x, then you get sin x which is periodic. However, the substitution still works as usual.
The cause of this trouble is a different constant of integration at different intervals.
Instead of +c for all real numbers, you actually have +c0 for -pi<=x<=pi, +c1 for pi<=x<=3pi, +c2 for 3pi<=x<=5pi, etc.
Actually, the functionPeriodicity is not the cause of this trouble. If you integrate cos x, then you get sin x which is periodic. However, the substitution still works as usual.
The cause of this trouble is a different constant of integration at different intervals.
Instead of +c for all real numbers, you actually have +c0 for -pi<=x<=pi, +c1 for pi<=x<=3pi, +c2 for 3pi<=x<=5pi, etc.
This is the 2021 integration marathon thread, as i have noticed users submitting integrals on previous year's threads.
I will start off:
1/(x+x^6)
sorry for bad formatting