Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I have a question regarding some simple integrals. For the life of my I cannot seem to get the right answer. I know the solution to the problem, but my answer seems to missing an ever so important (1/2) from the equation. Here is what I have:

The probelm is this, ∫tan^(-1)x dx.

[This is the indefinate integral of the inverse tangent of x]

When I work the problem out, my answer comes out to be:

xtan^(-1)x - ln|1+x²|+C

However, the answer that my professor and calculator give me is

xtan^(-1)x - (1/2)ln|1+x²|+C

Any thoughts of where this (1/2) is coming from?

To come to this answer, I first used integration by parts (uv-∫vdu) and used tan^(-1)x asuand (1/(1+x²)) fordu. I then took x^0 fordvand x asv.

The next substitution I made was to set x = tan(θ) which made dx = sec²(θ) dθ.

To find θ after I completed the integration, I made a triangle and found that sec(θ) was 1+x². Substituting that back into the equation gives me my final answer of:

xtan^(-1)x - ln|1+x²|+C.

I hope that explaination made sense. I can explain in more depth if needed.

Thank you,

Peter

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Help with integration

**Physics Forums | Science Articles, Homework Help, Discussion**