∫(1/(x^(1/6) +x^(1/3) ))dx=??


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Question Number 49134 by AdqhK ÐQeQqQ last updated on 03/Dec/18

$\int \frac{1}{x^{1 / 6} + x^{1 / 3}} d x = ? ?$
	Answered by arvinddayama01@gmail.com. last updated on 03/Dec/18

	$p u t x = t^{6}$ $d x = 6 t^{5} d t$ $6 \int \frac{t^{5}}{1 + t^{2}} d t$ $6 \int [t^{3} - t + \frac{t}{1 + t^{2}}]$ $6 \int t^{3} d t - 6 \int t d t + 3 \int \frac{2 t}{1 + t^{2}} d t$ $\frac{6}{4} t^{4} - \frac{6}{2} t^{2} + 3 l n (1 + t^{2}) + C$ $\frac{3}{2} t^{4} - 3 t^{2} + 3 l n (1 + t^{2}) + C$ $t = x^{1 / 6} v a l u e p u t t h e n$ $\frac{3}{2} x^{2 / 3} - 3 t^{1 / 3} + 3 l n (1 + x^{1 / 3}) + C$
	Commented by AdqhK ÐQeQqQ last updated on 03/Dec/18

	$t h a n k u s i r$
	Commented by arvinddayama01@gmail.com. last updated on 03/Dec/18

	$y o u r w e l c o m e$
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