Antiderivatives & Indefinite Integrals

[MitsuShai]

Homework Statement

Compute the following integral:

Homework Equations

none

The Attempt at a Solution

x^(1/2)-2(x^2)^(1/3) +1*x^(-1/4)dx =
(2/3)x^(3/2)-...I don't know this part...+x * (4/3)x^(3/4)
and this is where I stopped...

btw sorry I didn't put the symbols and stuff, I'm slow when it comes to technology...

 

[Gregg]

what level is this at?

 

[MitsuShai]

what level is this at?

Differential Calculus (calculus 1)

 

[Gregg]

is this the right integral?

$$\int \frac{x^{\frac{1}{2}}-2\left(x^2+1\right)^{\frac{1}{3}}}{x^{1/4}} \, dx$$

 

[Cyosis]

I don't think that integral is going to be possible without special functions.

 

[MitsuShai]

I don't think that integral is going to be possible without special functions.

O_O special funcitons?

 

[Cyosis]

Where did you get get this integral from and what is the question? Finding a 'normal' anti-derivative is not going to happen. So if this is a calculus one exercise there is more to it than you're telling us.

 

[MitsuShai]

Where did you get get this integral from and what is the question? Finding a 'normal' anti-derivative is not going to happen. So if this is a calculus one exercise there is more to it than you're telling us.

The question was "Compute the following integral: "

 

[Cyosis]

I don't see how you will be able to compute that integral at your level.

 

[Cyosis]

I see, while you may think this integral is nearly the same it is in fact much much easier. Just do the division and you get three trivial expressions.

 

[MitsuShai]

I see, while you may think this integral is nearly the same it is in fact much much easier. Just do the division and you get three trivial expressions.

ok then, what do you think?

∫ [x^(1/2) – 2*x^(2/3) +1] * x^(-1/4) dx

Distribute the x^(-1/4)
∫ x^(-1/8) – 2*x^(-1/6) + x^(-1/4) dx

Solve
(8/7)x^(7/8) – (12/5)x^(5/6) + (4/3)x^(3/4) + C , I entered that in but it's wrong...

 

[Cyosis]

The method is correct, but the arithmetic is not. For example 1/2-1/4 is not -1/8 and 2/3-1/4 is not -1/6.

 

[MitsuShai]

The method is correct, but the arithmetic is not. For example 1/2-1/4 is not -1/8 and 2/3-1/4 is not -1/6.

(x^(1/2))(x(-1/4) - (2x^(2/3))(x(-1/4)) + (x(-1/4)) = (x^(1/4)) - (2x^(5/12)+ x^(-1/4)
x^(1/4)-2x(5/12)+x^(-1/4)
(4/5)x^(5/4) - (24/17)x^(17/12) +(4/3)x^(3/4) + c

it's right, thank you :)