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

1 Answer
Monzur R.
May 19, 2017

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

Explanation:

#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"#

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