Indefinite Integrals

[dalukner]

The calculator gives the antiderivative shown in the first entry. The second entry is the antiderivative form I want. Is there any way to achieve this?

   

[Stevetuc]

(12-09-2019 06:35 AM)dalukner Wrote:  The calculator gives the antiderivative shown in the first entry. The second entry is the antiderivative form I want. Is there any way to achieve this?

This should generate the antiderivative result you want

Code:

int(x^(1/3)/x)

   

[Aries]

3*x^(4/3), I think you mean
The point here is, x^(1/3) is not the cubic root of x, that is true only for x>=0.
For x<0 the NthRoot function is not equivalent to ^(1/n).
Best,

Aries

[dalukner]

(12-09-2019 01:19 PM)Aries Wrote:  3*x^(4/3), I think you mean
The point here is, x^(1/3) is not the cubic root of x, that is true only for x>=0.
For x<0 the NthRoot function is not equivalent to ^(1/n).

Oops yeah that's what I meant. It was late at night. Is there another way to explain why the calculator does this? I don't fully understand. It makes more complex antiderivatives (and just about everything with fractional exponents) very messy.