Question

evaluate integral 1/ (x(sqrt(4x^2+1))) dx

Answer 1

\[\int\limits \frac{ 1 }{ x \sqrt{4x^2 +1} } dx\]

Answer 2

i would try a trig sub

Answer 3

I went through it all, and i got an answer. We don't have an answer key so i checked on wolfram and it the answer seems off a bit. I'll write down what i did.

Answer 4

beware of wolrams answers identical to yours via some tricky trickonometry

Answer 5

first i let \[x = \frac{ 1 }{ 2 }\tan \theta \]
\[dx =1/2 \sec^2\theta d \theta \]

so when i simplified it i got \[\int\limits \sec \theta/ \tan \theta\]

which also equals to \[\int\limits\limits \csc \theta\]

i used table and got -ln|cscx +cotx| + C

then i used trig to get theta into x

my final answer is \[-\ln \left| \frac{ \sqrt{2x^{2}+1} }{ 2x } +\frac{ 1 }{ 2x }\right| + C\]

Answer 6

is that correct?

Answer 7

the only thing I don't like is
sqrt(2x^2+1)

Answer 8

should be sqrt(4x^2+1)