A weird integration - or is it just me. (1 Viewer)

[currysauce]

From James Ruse 1993 Trial

2b)

Integrate (x²+1)/(x²+4) dx

thanks

 

[Mill]

From James Ruse 1993 Trial

2b)

Integrate (x²+1)/(x²+4) dx

thanks

Generally, when you have an integral with a numerator and denominator that look similar you want to transform one.

In this case:

(x²+1)/(x²+4) = (x²+4)/(x²+4) - (3)/(x²+4)

I think you can see where this is going now.

 

[acmilan]

You can use polynomial division, this gives (x²+1)/(x²+4) = 1 - 3/(x²+4). Then integrating that is routine.

Edit: Mill beat me to it

 

[haboozin]

From James Ruse 1993 Trial

2b)

Integrate (x²+1)/(x²+4) dx

thanks

I = x^2/(x^2 + 4) + 1/(x^2 + 4)

I = 1 - 4/(x^2 + 4) + 1/(x^2 + 4)

= x - 2tan^-1 x/2 + 1/2tan^1 x/2

= x - 3/2tan^1 x/2 + C

 

[currysauce]

thankyou

I got a new question

There are 5 girls and 6 boys in a group.

i) How many ways could they be arranged in a line such that each girl stands between 2 boys?

ii) How many arrangements are possible if 2 boys A and B stant at each end of the line?


THANKS

 

[mattchan]

thankyou

I got a new question

There are 5 girls and 6 boys in a group.

i) How many ways could they be arranged in a line such that each girl stands between 2 boys?

ii) How many arrangements are possible if 2 boys A and B stant at each end of the line?


THANKS

i) B G B G B G B G B G B
6! x 5! = 86400

ii) (A) G B G B G B G B G (B)
1 x 5! x 4! x 1 x 2 = 5760

Not sure if those two are right

 

[currysauce]

thanks

!!!