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guywithmath

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Indefinite Integrals

2∫tan³θdθ

and

∫(  ( 2x+12 ) / (x³-4x)  ) dx

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Indefinite Integrals

first, the easier of the two integrals, using the result that:

we have:

for the other, we can do:

so we have in the end:

note: that since

you could also have:

since the -1 difference is constant and can be included in the C, you could argue using secant instead of tangent is the integral in a simpler form, since then it only really involves the functions cosine and logarithm.

Last edited by luca-deltodesco (2008-11-29 21:40:37)

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Indefinite Integrals

Last edited by luca-deltodesco (2008-11-29 23:17:04)

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mathguy

Guest

Re: Indefinite Integrals

thank you delco that helps me out alot

theres one thing i dont understand though, when you get to the substitution. why use the substitution if you can already find what ∫tanθsec²θdθ

it seems like you have ∫tanθsec²θdθ and use substitution to make it into tan²θ-∫tanθsec²θdθ

i just dont get why you would use the substitution to get tan²θ-∫tanθsec²θdθ when you have the solution to ∫tanθsec²θdθ

thats the only part i dont get

mathguy

Guest

Re: Indefinite Integrals

and on the second one it was x³ not xsquared

although your solution helps me begin to solve it myself im not sure if im doing it correctly because of the ³

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Indefinite Integrals

It's integration by parts:

only, in this case it happens to be that:

and so, we end up with

For second one, taking the same approach again with partial fractions:

Last edited by luca-deltodesco (2008-11-30 08:52:23)

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mathguy

Guest

Re: Indefinite Integrals

luca-deltodesco thank you very much that helped alot

i now understand why you are a super member <3

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Indefinite Integrals

luca-deltodesco thank you very much that helped alot

i now understand why you are a super member <3

which one in his/her profile says that he's a super member?

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greg1313

Member

Registered: 2016-12-19

Posts: 20

Re: Indefinite Integrals

we have:

you could also have:

These are incorrect.  All of the forms involving the natural logarithm for the answer must have absolute value
bars where the logarithm of the quantity is being taken of in these examples, not just parentheses.

This goes for the rest of your posts in this thread.

Last edited by greg1313 (2017-06-13 08:34:20)