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Question Number 201817 by Calculusboy last updated on 13/Dec/23

Answered by witcher3 last updated on 13/Dec/23

$$=\int {\left(\sin \left(\ln (\mathrm{x}+1)\right)(\sqrt{\mathrm{x}+1}-1)\right)}^2\mathrm{dx}$$$$=\int {\sin }^2\left(\ln (\mathrm{x}+1)\right)(\mathrm{x}+2-2\sqrt{\mathrm{x}+1})$$$$\ln \left(\sqrt{\mathrm{x}+1}\right)=\mathrm{t}$$$$\mathrm{x}+1={\mathrm{e}}^{2\mathrm{t}}$$$$\iff \int {\sin }^2\left(2\mathrm{t}\right)({\mathrm{e}}^{2\mathrm{t}}+1-{2\mathrm{e}}^{\mathrm{t}}).{2\mathrm{e}}^{2\mathrm{t}}\mathrm{dt}$$$$\mathrm{basic}\mathrm{calculus}$$

Commented by justenspi last updated on 15/Dec/23

$$sirCanyouhelpmewiththis$$$$$$

Commented by justenspi last updated on 15/Dec/23

Commented by Calculusboy last updated on 15/Dec/23

$$\mathit{n}\mathit{i}\mathit{c}\mathit{e}\mathit{s}\mathit{i}\mathit{r},\mathit{i}\mathit{d}\mathit{o}\mathit{n}\mathit{g}\mathit{e}\mathit{t}\mathit{a}\mathit{m}$$

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