antiderivative of 1/(1+x^2) = integral of 1/(1+x^2) dx

set x = tan y
take derivative of both side so that you get
dx = (sec y)^2 dy

plug into the integral to get:
integral of 1/(1+(tany)^2) * (sec y)^2 dy

1 + (tany)^2 = (secy)^2

and then plug that into the integral to get

integral of 1/(secy)^2 * (secy)^2 dy = integral of dy
and that's equal to y + C

but we have to get that back in terms of x. to do that, we know x = tan y
which means y = arctan x

so in the end, integral of 1/(1+x^2) = arctan x + C

c is the constant (don't forget!!!)

Wow, I feel stupid now. I forgot that the derivative of arctan was already 1/(1 + x^2) OTL
Just wasted an hour of trying to figure it out to find that it was that simple all along...

I still understood your explanation though, making_mooz. Thank you! Both you & BoxBox.

[img]http://i.imgur.com/OkzQ4.png[/img]

I need help with my calc homework. i don't understand how i am to solve these two questions. if u can show steps it would be most appreciated .
question 1:
[img]http://i803.photobucket.com/albums/yy317/koolbklyn/1-1.png[/img]

Question 2:
[img]http://i803.photobucket.com/albums/yy317/koolbklyn/2-1.png[/img]

Crap...!
I totally forgot I had this ONE problem I didn't finish that's going to be on my test tomorrow. >.>
And my mind is blank.
Someone please explain to me how to solve this problem. lol (I know the answer is going to be ~5.4 because of the selected answers in the back of the book but I need to know HOW to get that answer.)

It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track?

♪MONSTARR~ will eat all your cookies and steal your bishies~♪ Φ_Φ

c=2(pi)r
Let's say c2 is the circumference of the outside, and c1 is the inside, r2 and r1 are the radii.
w is the width
w=r2-r1
c2-c1=3.4*10
2(pi)r2 - 2(pi)r1 = 34
2(pi) (r2-r1) = 34
2(pi)w = 34
w = 34/(2(pi))

Or I'm horribly wrong.

Quote from Sagaris

c=2(pi)r
Let's say c2 is the circumference of the outside, and c1 is the inside, r2 and r1 are the radii.
w is the width
w=r2-r1
c2-c1=3.4*10
2(pi)r2 - 2(pi)r1 = 34
2(pi) (r2-r1) = 34
2(pi)w = 34
w = 34/(2(pi))

Or I'm horribly wrong.

Thank you thank you thank you. D:
I feel stupid because now it seems easy...>.<
I misunderstood the problem...by width, I thought it meant the actual HUGE width of the track. (diameter of the bigger circle T.T)
Fail for me.

Thanks again~ (My friggin' teacher better not put this on the test. >.> We JUST learned arc lengths today.)

♪MONSTARR~ will eat all your cookies and steal your bishies~♪ Φ_Φ

I have to write a journal about The Adventures of Huckleberry Finn where I compare it with something outside of class... I already compared it with Dandelion Wine and also "Yes, the River Knows" by The Doors (yes, I know they have nothing in common 🤣 except maybe that they both use a river as a symbol?) in the last 2 weeks, but I have no idea what to write about for this week's... Especially as I'm already a little sleepy xD
Any ideas? It doesn't matter how stupid they are, I just need some inspiration xD

Quote from just-maya

Any ideas? It doesn't matter how stupid they are, I just need some inspiration xD

Well, you could just take the easy way out and use Tom Sawyer. Another Twain novel is also an option, as is Uncle Tom's Cabin. Go totally off and use any shounen manga with a strong coming of age bent. Go with another political satire like Candide or A Modest Proposal.

Now I feel dumb for not thinking of Uncle Tom's Cabin Especially as it happens to be one of the first books I ever read and the first to drop...
Anyway I just wanted to thank you for your answer, I'd probably use some of the ideas you gave next week, if we are still studying the same book. Writing about some shounen would be fun 🤣

ok now i have some problem T_T

i am supposed to write a program, that removes some characters(that is entered by user) from a loong string. for instance you ask user to enter a text like "masdapmepreds" then you want user to enter characters to be deleter like "sp". then the code should remove the wanted characters. and make it "madamered"

notes: * i am using C++ but please keep in mind that i am very beginner and even tutorials make no sense for me.
* both the lenght of entered text and characters to be deleted may change.
* code should only display the final result.
* i am only allowed to use these member functions of string "length, find, rfind, substr, at". so i cannot use "erase".

here is what i tried to do O_O

#include
#include
using namespace std;

int main ()
{ string text;
string deletes;

cin >> text;
cin >> deletes;

unsigned int length_deletes=deletes.length();
unsigned int begin=0;
string newtext="";
string character;

for (unsigned int k=0; k < length_deletes; k=k+1)
{ newtext = "";
begin = 0;
character=deletes.substr(k,1);
unsigned int length_text=text.length();

while (begin < length_text)
{ int placeofdelete = text.find(character, begin);
newtext=newtext+text.substr(begin, placeofdelete-begin);
begin = placeofdelete +1;

}

text = newtext;

}

cout << newtext << endl;

return 0;
}

i hope someone can tell where i do wrong in a simple way. mind i remind you that i am just a beginner 😢

How do I get the [NaOH] from adding an unknown [NaOH] to 0.0158642mol/L H2C2O4+2H2O? I've gotten that [H+] is 0.05552239mol/L in the original solution of oxalic acid dihydrase but then I take 25.00mL of it and neutralize it until pH 8.0, but I'm rather complete lost as to what to do next. Do I calculate original pH from before dilution or after dilution? Do I even need pH or can I just use ion [] to get how much [OH-]? (assuming H+ + OH- -->H2O) <---is this even right?

if your homework is about mathematical equations you should visit websites that would teach you how to do it...
that's what I'm doing,, what's the use of internet?
but if not..researching is the best.

Here's some websites I'm sure would help you...
I recommend....

...Mathway.com
...webmath.com
...yourteacher.com
😉

No ONGOING-STATUSES please.

Y'all are getting me excited for chemistry this year. 😀

Y'all are getting me sad/worried that I actually have to think again. 😔

[img]https://i.imgur.com/cWeUK2w.png[/img]

Quote from LawX

You are like the dense main character in a shoujo manga.

Quote from Crenshinibon

And you will murder someone one day, pika. If you're my daughter.

I need some help with my math homework.

I need to find out when the clock-hands will cover each other between 3 and 4 o'clock.
Can someone help me please? ><

Tom4toes!!!!
Chick3n!!!!
Fo0d!!!!