Calculus Help

[zoooom]

I would really appreciate it if someone could help me with this problem. I feel like it should be really easy, but I can't think of a way to do it.

indef. integral: sqrt(x)/sqrt(1+x^3)dx

Thanks a lot everyone.

 

[Trikat]

Great way to make a 1 post. 🙂

 

[JohnCU]

is that not a trig integral? 5 calculus classes and i can't remember.

 

[zoooom]

Heh, thanks.

 

[zoooom]

Originally posted by: JohnCU
is that not a trig integral? 5 calculus classes and i can't remember.

We haven't covered trig integrals yet (it's a summer school class), so I think there's another way to do it.

 

[JohnCU]

im too lazy to get out pen and paper but do you know integration by parts?

 

[zoooom]

Originally posted by: JohnCU
im too lazy to get out pen and paper but do you know integration by parts?

No, we haven't done that yet either. The class has only been going for a week now.

 

[ruffilb]

Originally posted by: JohnCU
is that not a trig integral? 5 calculus classes and i can't remember.

int of 1/(x^2 + 1)dx = arctanx

 

[JohnCU]

Originally posted by: zoooom

Originally posted by: JohnCU
im too lazy to get out pen and paper but do you know integration by parts?

No, we haven't done that yet either. The class has only been going for a week now.

oh okay i was trying to figure out where you were as to what kind of methods they would be testing you on.

 

[astrocase]

Simplify first. They're both Sqrts.

 

[ruffilb]

I know integration by parts should do it... idk if there's an easier way or not.

 

[ruffilb]

Originally posted by: astrocase
Simplify first. They're both Sqrts.

It doesn't reduce.

 

[zoooom]

Originally posted by: ruffilb

int of 1/(x^2 + 1)dx = arctanx

Can this be used to solve it somehow without integration by parts or trig integration?

 

[JohnCU]

playing with it now... sum of two cubes maybe

 

[ruffilb]

the answer, btw, is

(2ln((x^3+1)^(1/2)+ x^(3/2))/3)

 

[QED]

Originally posted by: ruffilb

Originally posted by: astrocase
Simplify first. They're both Sqrts.

It doesn't reduce.

I think she means trying to integrate sqrt( x / (x^3 + 1) ) instead of trying to integrate the equivalent sqrt(x) / sqrt( 1 + x^3) .

 

[JohnCU]

Originally posted by: zoooom

Originally posted by: ruffilb

int of 1/(x^2 + 1)dx = arctanx

Can this be used to solve it somehow without integration by parts or trig integration?

that's not integration using trig substitutions, it's just a simple integration formula for the inverse tangent function

 

[zoooom]

Originally posted by: ruffilb
the answer, btw, is

(2ln((x^3+1)^(1/2)+ x^(3/2))/3)

Now can you explain how to get that answer? lol

 

[JohnCU]

integral table

 

[ruffilb]

Originally posted by: JohnCU
integral table

CHEATER!

;-)

Originally posted by: zoooom

Originally posted by: ruffilb
the answer, btw, is

(2ln((x^3+1)^(1/2)+ x^(3/2))/3)

Now can you explain how to get that answer? lol

TI-89 FTW.

 

[zoooom]

Originally posted by: JohnCU
integral table

I don't see any that would work with this particular problem.

 

[zoooom]

Originally posted by: ruffilb

Originally posted by: JohnCU
integral table

CHEATER!

;-)

Originally posted by: zoooom

Originally posted by: ruffilb
the answer, btw, is

(2ln((x^3+1)^(1/2)+ x^(3/2))/3)

Now can you explain how to get that answer? lol

TI-89 FTW.

Bah!

 

[JohnCU]

Originally posted by: zoooom

Originally posted by: JohnCU
integral table

I don't see any that would work with this particular problem.

it's one of the integrals of sqrt(u^2+a^2) type with u = x^(3/2) and a = 1 just need to find out how to work in the other element

 

[Fenixgoon]

substitution doesn't work... at least u = 1+x^3 doesn't...

i guess parts... i just don't feel like working it out 😛

 

[ruffilb]

Oh man, if this is what I think it is, I LOVE these sorts of problems. It's complicated, but it's really cool.

I think it's a recursive integration by parts problem, where you have to pull over the int(Vdu) term to the other side and divide... can anyone confirm?