Question

How would you integrate (ln(x^2 + 1))/(x^2) dx

Answer 1

So I can write the question as \[\normalsize\color{blue}{ \int\limits_{ }^{ } \frac{\log(x^2+1)}{x^2}~dx} \]

Answer 2

okay ?

Answer 3

yes.

Answer 4

you need to integrate by parts, (using § for the integral sign)

§ f dg = fg - §g df

f= log (x²+1)
df = [2x ] / [ x²+1]
dg= 1/x² dx
g=-1/x

Answer 5

What I am getting here is,

[ -log(x²+1) ] /[ x ] + § [ 2 ]/[x²+1] dx

Answer 6

[ -log(x²+1) ] /[ x ] + § [ 2 ]/[x²+1] dx

[ -log(x²+1) ] /[ x ] + 2§ [ 1]/[x²+1] dx

[ -log(x²+1) ] /[ x ] + 2(tan^-1(x) ) + C

[ -log(x²+1) ]/x + 2tan^-1(x) + C

Answer 7

2tan^-1(x) - [ log(x²+1) ]/x + C

(switching the order)

Answer 8

It would take forever to do it in LATEX, sorry.

Answer 9

thank you very much! i was thinking of using trig substitution directly and forgot about integration by parts...

Answer 10

Anytime... also, once you mentioned trig, I'll tell you that it is the highest level course in math that I took.

yw !