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Question Number 113565 by bemath last updated on 14/Sep/20

Answered by bobhans last updated on 14/Sep/20

$$\int ({5\mathrm{x}}^2+10){({\mathrm{x}}^3+6\mathrm{x})}^3\mathrm{dx}=$$$$\int 5({\mathrm{x}}^2+2){({\mathrm{x}}^3+6\mathrm{x})}^3\mathrm{dx}=$$$$[\mathrm{u}={\mathrm{x}}^3+6\mathrm{x}\Rightarrow \mathrm{du}={3\mathrm{x}}^2+6\mathrm{dx}]$$$$\int 5{\left(\mathrm{u}\right)}^3\left(\frac{1}{3}\mathrm{du}\right)=\frac{5}{3}\int {\mathrm{u}}^3\mathrm{du}$$$$=\frac{5}{12}{({\mathrm{x}}^3+6\mathrm{x})}^4+\mathrm{c}$$

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