How do you find the indefinite integral of $int 1/(x^(2/3)(1+x^(1/3))$ ?

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Answer 1 · 2017-05-19T21:10:03

$A(x)=3ln|root(3)x+1|+"c"$

$int 1/(x^(2/3)(1+x^(1/3))$ $dx$

$=3int x^(-2/3)/(3(1+x^(1/3))$ $dx$

We now have the integrand in the form $(f'(x))/f(x)$ . Using the reverse chain rule, we know that the integrals of these forms are $ln|f(x)|+"c"$ .

$therefore int 1/(x^(2/3)(1+x^(1/3))$ $dx=3ln|root(3)x+1|+"c"$

How do you find the indefinite integral of int 1/(x^(2/3)(1+x^(1/3))int 1/(x^(2/3)(1+x^(1/3))?