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Question Number 145259 by mathdanisur last updated on 03/Jul/21

$$\int \frac{{(3\sqrt{x}+2)}^5}{\sqrt{x}}dx=?$$

Answered by Dwaipayan Shikari last updated on 03/Jul/21

$$put\sqrt{x}=t\Rightarrow \frac{1}{2\sqrt{x}}dx=dt$$$$=2.3^5\int {(t+\frac{2}{3})}^{5}dt$$$$=3^4{(t+\frac{2}{3})}^6+C=81{(\sqrt{x}+\frac{2}{3})}^6+C$$

Commented by mathdanisur last updated on 03/Jul/21

$$thanksSer$$$$Answer:\frac{1}{81}{(3\sqrt{x}+2)}^6\mathit{o}\mathit{r}\frac{1}{9}{(3\sqrt{x}+2)}^6?$$

Commented by Dwaipayan Shikari last updated on 03/Jul/21

$$\frac{1}{9}{(3\sqrt{x}+2)}^6+C$$

Commented by mathdanisur last updated on 03/Jul/21

$$Ser,butinyoursolution81{(\sqrt{x}+\frac{2}{3})}^6$$

Commented by Dwaipayan Shikari last updated on 03/Jul/21

$$81{(\sqrt{x}+\frac{2}{3})}^6=\frac{3^4}{3^6}{(3\sqrt{x}+2)}^6=\frac{{(3\sqrt{x}+2)}^6}{9}$$

Commented by mathdanisur last updated on 03/Jul/21

$$ThanksSer$$

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