Indefinite Integral of 1/x^2/3(1+x^1/3) | Homework Equations & Solution

[fluxions22]

Homework Statement

integral of 1/x^2/3(1+x^1/3)

Homework Equations

integral of 1/x dx = ln|x| + c

The Attempt at a Solution

let u= x ^2/3(1+x^1/3)

 

[fluxions22]

note: the stated relevant equation may actually be 1/u du = ln |u| + C not sure

 

[Mark44]

Homework Statement

integral of 1/x^2/3(1+x^1/3)

This is very ambiguous. What exactly is the integrand?

Homework Equations

integral of 1/x dx = ln|x| + c

The Attempt at a Solution

let u= x ^2/3(1+x^1/3)

 

[fluxions22]

the problem is 1 divided by x^2/3(1+x^1/3) dx

the integral is indefinite

 

[fluxions22]

i don't think it calls for u substitution on further review

 

[Mark44]

the problem is 1 divided by x^2/3(1+x^1/3) dx

This is still very ambiguous.
This is what you wrote, but not what I think you meant.
$$\frac{1}{\frac{x^2 (1 + \frac{x^1}{3})}{3}}$$

 

[fluxions22]

the ^ sign stands for "to the power of" but if i express the problem in words it would be "one divided by x to the 2/3 power times (1 plus x to the one thirds power)

 

[Mark44]

Then you should write the integrand as 1/[x^(2/3)(1+x^(1/3))]. Note the parentheses around the exponents.

Better yet, here's the LaTeX for your integral:
$$\int \frac{1}{x^{2/3}(1 + x^{1/3})} dx$$

I would start with an ordinary substitution, u = x^1/3. I doubt very much that this will turn into du/u.

 

[physicsman2]

Then you should write the integrand as 1/[x^(2/3)(1+x^(1/3))]. Note the parentheses around the exponents.

Better yet, here's the LaTeX for your integral:
$$\int \frac{1}{x^{2/3}(1 + x^{1/3})} dx$$

I would start with an ordinary substitution, u = x^1/3. I doubt very much that this will turn into du/u.

Then try u = 1+ x^1/3, that should do it. I don't think that's too much help, is it?

 

[fluxions22]

if u is 1+ x^1/3 then ln |1+x^1/3| + C is correct?

 

[Mark44]

Not quite. If u = 1 + x^(1/3), du = dx/(3x^(2/3)). Your answer needs to account for that factor of 3 in the denominator.

Note that x^1/3 $\neq$ x^(1/3). The first is the same as x/3. When you have fractional exponents USE PARENTHESES!