Question

Please help me find the anti-derivative of 1/(4+x^2)

Answer 1

First try to recognize, what kind of integral do you think it might be? it is a division obviously, so what options do you have?

Answer 2

look for an inverse trig function?

Answer 3

yes

Answer 4

arctan is probably the closest. but what do I do with the 4 in the denominator?

Answer 5

It might help you to remember the structure of the derivatives of inverse trigonometric functions.

Answer 6

you are correct

Answer 7

divide the whole expresion by 4, and put 1/4 outside the integral

Answer 8

\[\frac{ 1 }{ 4 } \int\limits \frac{ 1 }{ 1+\frac{ x^2 }{ 4 } }\]

Answer 9

dx

Answer 10

you can't invent anything in math, so you put 1/4 out as a testimonial of what you are doing

Answer 11

you're third to last post says [Math Processing Error]

Answer 12

wait

Answer 13

\[\frac{ 1 }{ 4 } \int\limits \frac{ 1 }{ 1 + \frac{ x^2 }{ 4 } } dx\]

Answer 14

\frac{ 1 }{ 4 } int \frac{ 1 }{ 1 + \frac{ x^2 }{ 4 } } dx

Answer 15

I also remind you that the derivative of the arctg is \[\frac{ 1 }{ 1+ (SOMETHING)^2 } ·[SOMETHING]'\]

Answer 16

so now that you have divided by 4, what else do you need to be able to apply the formula?

Answer 17

You're equations are not coming through clearly, they look like this...\frac{ 1 }{ 4 } int \frac{ 1 }{ 1 + \frac{ x^2 }{ 4 } } dx

Answer 18

ok wait

Answer 19

can you see it now?

Answer 20

ya that works

Answer 21

ok, now i remind you of the form of the derivative of the arctg

Answer 22

we already got the 1+ (something) we were looking for, what do you think we can do next?

Answer 23

idk, is it multiplied by (x^2)/4

Answer 24

no, i got a hint for you

Answer 25

x^2/4 is like if it was ALREADY squared