Question

int[1, 3] 1/(x^3+x) dx

Answer 1

\[\int\limits_{1}^{3} \frac{1}{(x^{3}+x)} dx\]

Answer 2

partial decomp by chance?

Answer 3

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

Answer 4

\[\frac{ 1 }{ x } - \frac{ x }{ x^{2}+1 }\]

Answer 5

how would i integrate \[\frac{ x }{ x^{2}+1 }\] ?

Answer 6

\[\int\limits_{}(1/x) dx=\log(x)\]

Answer 7

Dx[x^2+1] = 2x, so your missing a 2. multiply by 2/2 and borrow it from that

Answer 8

\[\int\limits_{}^{}x/(x ^{2}+1) dx\]
put x^2=t
2x dx= dt
the integral reduces to

Answer 9

\[(1/2)\int\limits_{}^{}1/(1+t) dt\]

Answer 10

any confusion?/

Answer 11

yeah partial decomp or long division

Answer 12

ahh, thank you! i should be fine from here on!

Answer 13

you are welcome....!!!!