Question

Integrate this...

Answer 1

\[\frac{ 10x^2+15x }{ (x)(1+x^2)(x+2) }\]

Answer 2

factorise the numerator and look to cancel common factors, before integrating

Answer 3

You can use partial fraction decomposition.

Answer 4

weird that there is a common factor of \(x\) top and bottom

Answer 5

I used partial fraction and got....

9arctan(x)-ln(|x+2|)+C

Answer 6

yes, I cancelled out the x and factored out a 5 and pulled it outside of the integral

Answer 7

My partial fraction was...

\[\frac{ 2x+3 }{ (1+x^2)(x+2)}=\frac{ A }{ x+2 }+\frac{ Bx+C }{ 1+x^2 }\]

Answer 8

Then got...\[\frac{ -1 }{ 5 }(\frac{ 1 }{ x+2 })+\frac{ 9 }{ 5 }(\frac{ 1 }{ 1+x^2 })\]

Answer 9

then I integrated those two separately, put the 5 back in and got the answer above.

Answer 10

I'm not sure if I did that correctly or not.