วีดีโอ

what this kid trying do tell? bruh nobody can learn how do a snake ball from watching ur video

please learn the basics of integration first then solve these

Editing as I follow along: for the first one, not much to say you did it perfectly. For the second one also not much to say but to optimize for time you could have just done the power reduction right off the bat and gotten integrals of 1/2 of (1/2)cos(4x) and gotten the same result without the extra U-sub. So far so good! You are improving! EDIT2: I want you to recall something from your algebra days (a^3 + b^3) = (a+b)(a^2 - ab + b^2) and x^3 + 1 = x^3 + 1^3 so x^3 + 1 = (x + 1)(x^2 - x + 1) NOW do the partial fraction decomposing and you end up with 1/3 times integrals of 1/(x + 1) minus 1/3 times integral of (x-2)/(x^2 - x + 1) The first one is just (1/3)ln|x + 1| the second is a slightly more tricky one notice how the derivative of the bottom would be 2x - 1, our goal is to break up the fraction in a way where the derivative of the bottom works to our advantage in a U sub so multiply by 2/2 and push out the 1 half while putting the 2 in the numerator to get (1/6) times integral of (2x - 4)/(x^2 - x + 1) now break apart the fraction into (2x - 1)/(x^2 - x + 1) + (-3)/(x^2 - x + 1) It is now (1/3)ln|x + 1| - (1/6)ln|x^2 - x + 1| + (1/2) times integral of 1/(x^2 - x + 1) for this final one complete the square and you end up with (root(3)/3)tan^-1((2/root(3))(x - (1/2))) So the final answer is as follows (1/3)ln|x + 1| - (1/6)ln|x^2 - x + 1| + (root(3)/3)tan^-1((2x - 1)/root(3)) + C EDIT3: use integration by parts. Set u = x so du = dx and dv = sin^2(x)dx so v = (1/2)(x) - (1/4)sin(2x) so it’s (1/2)x^2 - (1/4)(x)sin(2x) - integral of (1/2)x - (1/4)sin(2x) which comes out to (1/2)x^2 - (1/4)(x)sin(2x) - (1/4)x^2 - (1/8)cos(2x) = (1/4)x^2 - (1/4)xsin(2x) - (1/8)cos(2x) + C EDIT4: nice job on getting 2 in a row right. You did them perfectly. Nice job! as for the cot^5(x) that’s the same as cos^5(x)/sin^5(x) = (cos(x)cos^4(x))/sin^5(x) cos^4(x) = [1 - sin^2(x)]^2 now let u = sin(x) so du = cos(x)dx the integral becomes (u^4 - 2u^2 + 1)/u^5 with respect to u Break apart the fraction and integrate and you get ln|sin(x)| + csc^2(x) - (1/4)csc^4(x) + C

I’m editing this as I follow along. for the first one, multiply by e^-x on top and bottom to force a trig sub. It becomes (e^-x)/(1 + e^-2x) let u = e^-x so du = -e^-xdx the e^-x cancel and you are left with the integrals of -1/1 + u^2 = -tan^-1(u) = -tan^-1(e^-x) + C This can also be written as cot^-1(e^-x) + C (either will satisfy the integral). EDIT: for the second one, whenever there’s an integral of a logarithm involved you should always think integration by parts. Set u = log2(x) so du = 1/xln(2) set dv = 1dx so v = x so it’s xLog2(x) - integrals of 1/ln(2) = xLog2(x) - x/ln(2) + C

I’m following along. This comment will be updated as I watch. So right off the bat I have thoughts. Whenever you have an integral with sec(x) and tan(x) you immediately want to take a sec(x)tan(x) out so you can do a sec(x) u sub with trig identities to turn the tan(x) into a sec(x) so what you should have done was set u = sec(x) so du = sec(x)tan(x)dx now the integral is tan^4(x)sec^2(x) tan^4(x) = (sec^2(x) - 1)^2 So the who’s this is now integral of (u^2 - 1)^2(u^2) = integral of u^6 - 2u^4 + u^2 So the final answer is (1/7)sec^7(x) - (2/5)sec^5(x) + (1/3)sec^3(x) + C EDIT: question 2: nice job! question 3: yikes! but here we go. You need to factor the bottom and do a partial fraction, because it’s a quartic it’s gonna be insanely annoying. I managed to get it to the integral of 1/2(x^2 - root(3)x + 1) + 1/2(x^2 + root(3)x + 1) On each of these you complete the square. (This is where it gets really messy so bear with me). 2 times the integral of 1/(4(x + root(3)/2)) + 1) and 2 times integral of 1/(4(x - root(3)/2) + 1) substituting 2x + root(3) = tan(y) for the first dx = (1/2)sec^2(y) and substituting 2x - root(3) = tan(y) for the second dx = (1/2)sec^2(y) the final answer is tan^-1(2x + root(3)) + tan^-1(2x - root(3)) + C That one was quite tough! I don’t blame you for not getting it (I almost didn’t either). Edit 2: I give up on the 1/(1 + x^5) EDIT3: for the 4(x + e^x)^2 just foil it. so it’s the integral of 4x^2 + 8xe^x + 4e^2x and the integral of that is (4/3)x^3 + 8xe^x - 8e^x + 2e^2x I cleaned it up a bit and got (4/3)x^3 + e^x[e^x + 8x - 8] + C EDIT: csc^3(x)sec(x) = 1/(sin^3(x)cos(x)) and 1 = cos^2(x) + sin^2(x) So you can break it down into two integrals. One of cos(x)/sin^3(x) which is just (-1/2)(1/sin^2(x)) = (-1/2)csc^2(x) the other one is 1/sin(x)cos(x) and this can be again broken down if you substitute cos^2(x) + sin^2(x) for 1 and now it’s the integral of tan(x) + cot(x) which get you ln|sec(x)| + ln|sin(x)| which is ln|tan(x)| by property of logarithms. So the final answer here was (-1/2)csc^2(x) + ln|tan(x)| + C Hope this was helpful. As you can tell I’m not perfect at this because I couldn’t get the 1/(1 + x^5) but I have a decent amount of experience of calc I, II, III and differential equations so Ive seen a fair bit of stuff with integrals. That 1/(x^5 + 1), I will keep trying on it but hopefully one of your other viewers cracks it before me. Have a nice day! I’m definitely subbing.

oh my god I completely missed this

instantly subbed

this made me love math even more

This is trash

To fast

I really have to put this in the slowest setting in order for it to look like normal speed

THIS is one of the worst tutorials to exist

This is kind of fast

Ya you make it so fast

It’s not even a ball 🥚

You are going to fast

I think it is too fast

Your hands in the way

This is not a tutorial it a “ hey guys look what I made😂

Bro this does not help this is not even a tutorial you’re just speed running it

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Why is it so fast i can barely keep up with the pace and its so blurry

If this was a tutorial it sucked

It looks like an egg, not a ball

I thought you were atharva the one with the bird pfp thingy

this video brightened my day

Truly a tutorial of all time

ZOOM IN

Can you do it slow

BRO IS SPEED RUNNING HOL UP

bro i can’t see anything

Nice

LoL

Too fast

You cover it and you go so fast you need to work on that

What kind of “how to” video goes this fast

Hay

Nice

horrible tutorial

You have a dog?

Good job Atharva!!!

I’m not trying to be rude but I hate this tutorial 1:it’s to fast and playback speed isn’t helping 2: it doesn’t make sense 3:their hands are in the way

stop going so fast

I didn't realize that I clicked on a speed run of this.. I was looking for a tutorial lol. Even when you slow the video down its still hard to see and keep up with this.

Slow down

MY MANNN its me gus remember me?

Can’t even see the angle and it’s too hard to tell what your turning so what’s the point of this