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What is the antiderivitive of ln(1 + t^2)?

Here, let's notationalize the problem to make it easier:

{ [ ln(1+t^2) dt ]

Sorry, can't offer help

<---totally bombed a Calc test yesterday. 🙁 S2pid integration!
 
hah. i hear that. I totally bombed a calc final today. (stupid fluid pressure)

what calc level is this? ie should we even be trying?
 
y = ln(1 + t^2)
e^y = e^ln(1 + t^2)
e^y = 1+t^2
--integrate both sides, i'm too lazy to finish this off.

I have a Calc BC final tommorow, I thought I'd show off my integration skills 🙂
 
what calc level is this? ie should we even be trying?

Calc BC. Screwed up badly because of stupid area and volume of disk/washer problems 🙁
 
I know this thread is two days old, but I need a challenge. 🙂

Integral [ln(1+t^2)]dt

let u=ln(1+t^2)
du=[2t/(1+t^2)]dt

dv=dt
v=t

t*ln(1+t^2) - Integral [(2t^2)/(1+t^2)]dt

Integral [(2t^2)/(1+t^2)]dt

let x=tan(A)
therefore dx=sec^2(A)dA

2*Integral [(tan^2(A)*sec^2(A))/(sec^2(A))]dA
2*Integral tan^2(A)dA
2*Integral sec^2(A)dA - 2*Integral(1)dA
2*tan(A)-2(A)
2[x-arctan(x)]

Therefore,

t*ln(1+t^2) + 2[arctan(x)-x] + C
 
Yea well, it's been awhile since I worked these kinds of questions and math never was my best subject. 🙂 Heck, I'm not even sure if I did this type of problem?
 
hah you think this is hard?

I got a 4 on the AP calc exam last year and then took Calc 3 (multi variable) in college. More than 2 variables = Harder than anything you will ever do!
 


<< hah you think this is hard?

I got a 4 on the AP calc exam last year and then took Calc 3 (multi variable) in college. More than 2 variables = Harder than anything you will ever do! >>


Why the heck are you bragging? Calculus III is not exactly an advanced math class.
 
i got a 5 on calc BC... multivariable calculus is not difficult nor was it very enlightening to the world of calculus. all it does is give you the tools for partial differential equations. which is significant. it's been 5-6 years since i did BC calc and even I was able to solve this problem. (no one ever remembers trig subs, so everyone who needs them have charts and tables =)))))

tip: the key to MOST, if not all, logarithmic integrals is the use of division by parts. the existence of "1+tt" tells you that trig substitutions may be used, same if you see sqrt(1+tt)

--

this is commonly seen in calc2, or second semester calculus. where you learn more advanced integration methods, such as integration by parts, and trig subs. as well as infinite series where you learn that e^(i*pi) + 1 = 0 as the unifying equation for... trancendental, nothing, real\integer\rational, imaginary numbers =)
 
i am SO glad i escaped my two semesters of calc in my freshman year with a B average... two years later, I've forgotten it all.
 
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