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/sci/ - Science & Math

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4145295 No.4145295 [Reply] [Original]

Integrate sec (x) . tan^-1 (x)
(integrate by parts)

>> No.4145298

Wolfram

>> No.4145342

>>4145298
I checked the integral and derivative of each, and they didn't match up to cancel shit out. I then just told Alpha to integrate it, and it told me it couldn't. I'm guessing this is a troll question.

Anyway, the definite integral of this thing from 0 to 1 is approximately 0.585741.

>> No.4145346

>>4145342
You cannot integrate tan^-1 x
That's where i went wrong.

Thanks anyway.

>> No.4145351

Is that "inverse tangent" or "one over tangent"?

>> No.4145354

>>4145351
inverse.

>> No.4145361
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4145361

Integration by parts sounds like a Calculus A topic, but with inverse trig functions it gets complicated. Are you sure you aren't supposed to be taking the derivatives or something like that?

>> No.4145387

Not OP, but is integrate and antiderivative the same thing?

>> No.4145402

>>4145387
Yes. This is called the fundamental theorem of calculus.

>> No.4145404

>>4145387
Some functions have a antiderivative but aren't integratable and some integratable functions don't have a antiderivative.
OP probably wants to find an antiderivative.

>> No.4145417

>>4145295
got it

uv' = uv int u'v

let u = sec x
let v' = tan^-1 x

sec x . ((x tan^-1 x) - 1/2 log((x^2) +1)) - int ((tanxsecx) . (x tan^-1 x) -1/2 log ((x^2 + 1))

cont.

>> No.4145427

>>4145417
Okay. I don't have a clue where i'm going with this.

>> No.4145428
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4145428

>>4145402
>>4145404
Okay

>> No.4145523

>>4145404
>some integratable functions don't have a antiderivative
right
>Some functions have a antiderivative but aren't integratable
I was going to say the fundamental theorem of calculus said otherwise, but I checked and I'm wrong. Can you provide an example though?

>> No.4145542
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4145542

>>4145523

>> No.4145579

>>4145542
Thanks. I had forgotten an unbounded function couldn't be riemann integrable but it makes sense.