Question

can someone help me with this integral. I will write it.

Answer 1

\[\int\limits_{}^{} (4.5)/(1+9x^2)\]

Answer 2

Now i am familiar with this:

\[\int\limits_{}^{}(dx)/(a^2+x^2)=(1)/(a)\arctan(x)/(a)+c\]

Answer 3

but, how do i go about solving this, ans what does the letter a stand for?

Answer 4

Okay Good You have

\[ \int 4.5 \frac{1}{1 +9x^2}\]
Now try taking 9 common

Answer 5

\[4.5 \int \frac{1}{9} \frac{1}{\frac{1}{9} + x^2}\]

Answer 6

9x^2 could be written as (3x)^2

Answer 7

now where does that 1/9 come from

Answer 8

\[\frac{4.5}{9} \int \frac{1}{\frac{1}{9} +x^2}\]

Answer 9

when you take 9 common from \(1 + 9x^2\) it becomes \( 9(\frac{1}{9} +x^2)\)

Answer 10

i see that

Answer 11

so, that 1/a would be 1/9 or 4.5/9?

Answer 12

Now
\[\frac{1}{2} \int \frac{1}{\frac{1}{3^2} +x^2} \]
A is \(\frac{1}{3} \)

Answer 13

x = (1/3)tan(u)
dx = (1/3)sec^2 du

\[4.5\int\limits_{}^{}\frac{(1/3)\sec^{2}u}{1+9(1/9\tan^{2}u)} = 4.5\int\limits_{}^{}\frac{(1/3)\sec^{2}u}{\sec^{2}u} = \frac{4.5}{3}\int\limits_{}^{}du\]

Answer 14

oh

Answer 15

Hence the Integral is \( \frac{1}{2} \times {3} tan^{-1}3x\)

Answer 16

i go the answer as being (3/2)(tan ^-1)3x+c

Answer 17

Oh YEA I forgot the C constant

Answer 18

dumbcow, how is it that you let x be (1/3)tan u, i dont see where you got that?

Answer 19

its just a trig substitution
i noticed that 1+tan^2 = sec^2
so making x=1/3tan(u) works

Answer 20

but you saw that 1+tanx^2=sec^2, okay, but hoe does that translate to (1/3)tan

Answer 21

i get confused sometimes if i try to follow the formula...lol

well you have to turn 9x^2 into tan^2
(1/3)^2 = 1/9
1/9*9 = 1

Answer 22

that looks, good, i will write it down. Thanks

Answer 23

no problem

Answer 24

i have a question. For ishann or dumbcow, how did we get the the 3 in 3tan ^-1??

Answer 25

Try to do the question once again : )

Answer 26

and what happens to the 1/2 that is outside of the integral??

Answer 27

4.5/3 = (9/2)/3 = 9/6 = 3/2

Answer 28

now, can you looks at ishaan method, what did he do witht he 1/2 ?

Answer 29

oh i see
A = 1/3 right
well in the formula...it has (1/A) as coefficient
1/A = 1/(1/3) = 3
the 1/2 stays on outside til after integration then is just multiplied to the 3

Answer 30

oh, i got it, a is 1/3 but that in the formula a is actually 1/a which means i have to flip it and it becomes 3/1 which the is multiplied by the 1/2 that was out side

Answer 31

thanks again dumbcow, if i could give you another medal i would

Answer 32

thanks

Answer 33

i think im done...goodnight

Answer 34

see ya