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Question Number 69623 by aliesam last updated on 25/Sep/19

$$\int \frac{1}{\sqrt{x}+\sqrt[3]{x}}dx$$

Answered by MJS last updated on 25/Sep/19

$$\mathrm{we}\mathrm{had}\mathrm{this}\mathrm{before}...$$$$\int \frac{dx}{x^{1/2}+x^{1/3}}=$$$$[t=x^{1/6}\to dx=6x^{5/6}dt]$$$$=6\int \frac{t^3}{t+1}dt=6\int (t^2-t+1-\frac{1}{t+1})dt=$$$$=2t^3-3t^2+6t-6\ln (t+1)=$$$$=2x^{1/2}-3x^{1/3}+6x^{1/6}-6\ln (x^{1/6}+1)+C$$

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