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Question Number 112773 by 675480065 last updated on 09/Sep/20

$$\int \frac{\sqrt{x}}{x^3+1}dx$$$$Pleasehelp$$

Answered by MJS_new last updated on 09/Sep/20

$$\int \frac{\sqrt{x}}{x^3+1}dx=$$$$[t=x^{3/2}\to dx=\frac{2dt}{3\sqrt{x}}]$$$$=\frac{2}{3}\int \frac{dt}{t^2+1}=\frac{2}{3}\arctan t=$$$$=\frac{2}{3}\arctan x^{3/2}+C$$

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