<s>[INST] How to calculate the indefinite integral of $\frac{1}{x^{2/3}(1+x^{2/3})}$? 
$$\int \frac{dx}{x^{2/3}(1+x^{2/3})}.$$

I substituted,
$$t=\frac{1}{x^{1/3}}$$
$$\frac{dt}{dx} = -\frac{1}{3x^{4/3}}$$
$$\frac{dt}{dx} = -\frac{t^4}{3}$$
Rewriting the question,
$$\int \frac{dx}{x^{2/3}+x^{4/3}}$$
$$-\frac{1}{3} \int \frac{dt}{t^4\Bigl(\frac{1}{t^2}+\frac{1}{t^4}\Bigr)}$$
We have,
$$-\frac{1}{3} \int \frac{dt}{t^2 + 1}$$
$$-\frac{1}{3}\tan^{-1}t+C$$
$$-\frac{1}{3}\tan^{-1}\Biggl(\frac{1}{x^{1/3}}\Biggr)+C$$
But the answer given is $$3\tan^{-1}x^{1/3}+C$$
Where am I wrong?
Any help would be appreciated.
 [/INST] $t=\sqrt[3]{x},\qquad dt=\frac{1}{x^{2/3}}dx$
$$\int \frac{1}{x^{\frac{2}{3}}+x^{\frac{4}{3}}}dx=3\int \frac{1}{t^2+1}dt$$
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