Question

Integral of x/(x^2+1) from 3 to 1?

Answer 1

\[\int\limits_{1}^{3}\frac{ x }{ x^2+1 }dx\]
?

Answer 2

i set u = x^2 +1
and the answer i got was 1/2 ln 10
but the answer the book showed was 1/2 ln 5
can someone please explain?

Answer 3

\[\int\limits_{3}^{1}\frac{ x }{ x ^{2}+1 }=\]

Answer 4

u=x^2+1 so du=2x

Answer 5

yeah

Answer 6

\[\frac{ 1 }{ 2 }*\int\limits_{3}^{1}\frac{ 1 }{ u }du\]

Answer 7

that's ln(u)

Answer 8

1/2*ln(x^2+1) from 3 to 1

Answer 9

1/2ln(10)-1/2ln(2)

Answer 10

1/2 ln u
1/2 ln (x^2+1) from 1 to 3
which would just be 1/2 ln 10
right?
the limits are from 1 to 3, not 3 to 1

Answer 11

so, it is 1/2*ln(10/2)=1/2*ln(5)

Answer 12

ohhh wow. i added wrong.

Answer 13

thanks anyways :)