x-x-3-1-dx-Please-help-

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

\int \frac{\sqrt{x}}{x^{3} + 1} d x

P l e a s e h e l p

Answered by MJS_new last updated on 09/Sep/20

\int \frac{\sqrt{x}}{x^{3} + 1} d x =

[t = x^{3 / 2} \to d x = \frac{2 d t}{3 \sqrt{x}}]

= \frac{2}{3} \int \frac{d t}{t^{2} + 1} = \frac{2}{3} \arctan t =

= \frac{2}{3} \arctan x^{3 / 2} + C

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