Question

1) x^2+1/6x-9x^2 dx
2) xdx/2+6x+9x^2
3) 1/x^2-1 dx

Answer 1

What are you supposed to to?

Answer 2

Find antiderivative

Answer 3

Oh

Answer 4

An antiderivative of a function f is a function whose derivative is f . In other words, F is an antiderivative of f if F' = f . To find an antiderivative for a function f , we can often reverse the process of differentiation.

For example, if f = x^4 , then an antiderivative of f is F = 1/5 x^5 , which can be found by reversing the power rule. Notice that not only is 1/5 x^5 an antiderivative of f , but so are 1/5 x^5 + 4 , 1/5 x^5 + 6 , etc. In fact, adding or subtracting any constant would be acceptable.

Answer 5

That I get, but I just don't know how we antideriverate those functions

Answer 6

Ok,
First try to antideriverate them without the numbers.

Answer 7

Also to do it part by part.
So the first one do the numirator and then the denominater.

Answer 8

Just do the same thing on all three.

Answer 9

What, I don' get what u mean?

Answer 10

For the first one do x^2+1
After that do 6x-9x^2

Answer 11

For the second one do x
Then do 2+6x+9x^2

Answer 12

Then for the last one do 1first
Then do x^2-1

Answer 13

So...
The first one will be
\[\frac{ \frac{ x^3 }{ 3 }+x }{ 3x^2 -3x^3}\]
The second one should be
\[\frac{ \frac{x^2 }{ 2 } }{ 2x+3x^2 +3x^3}\]
And the third one should be
\[\frac{ x }{ \frac{ x^3 }{ 3 } -1 }\]

Answer 14

first one is \( \int \dfrac{x^2+1}{6x-9x^2} dx\) right??

if so you need to use some algebra, eg partial fractions, to simplify that and make it fit some known integration patterns

i'd just pile in with with long division as this stuff can get really, really tedious after a while

so you have \(\dfrac{x^2+1}{6x-9x^2} = \dfrac{1}{x}\dfrac{x^2+1}{6-9x}\) and why not try \((x^2 + 1) \div (-9x + 6)\) in ye olde long division format

Answer 15

Oh lawd jesus.

ain't nobody got time for that!

Answer 16

LOL

Answer 17

the first on i say

Answer 18

PS

this is a really good resource
http://www.mathsisfun.com/algebra/partial-fractions.html