Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 68699 by Rio Michael last updated on 15/Sep/19

$$\int ln(x+4)dx=$$

Commented by mathmax by abdo last updated on 15/Sep/19

$$letI=\int ln(x+4)dxchangementx+4=tgive$$$$I=\int lntdt=tln\left(t\right)-t+c=(x+4)ln(x+4)-x-4+c$$

Commented by Cmr 237 last updated on 15/Sep/19

$$\mathrm{posons}\ln (\mathrm{x}+4)=\mathrm{t}\mathrm{on}$$$$\mathrm{x}={\mathrm{e}}^{\mathrm{t}}-4,\mathrm{dx}={\mathrm{e}}^{\mathrm{t}}\mathrm{dt}\mathrm{ainsi},$$$$\int \ln (\mathrm{x}+4)\mathrm{dx}=\int {\mathrm{te}}^{\mathrm{t}}\mathrm{dt}$$$$=\left[{\mathrm{te}}^{\mathrm{t}}\right]-\int {\mathrm{e}}^{\mathrm{t}}\mathrm{dt}$$$$=(\mathrm{t}-1){\mathrm{e}}^{\mathrm{t}}+\mathrm{c},\mathrm{c}\in \mathbb{R}$$$$=(\mathrm{x}+4)[\ln (\mathrm{x}+4)-1]+\mathrm{c}$$

Answered by Prithwish sen last updated on 15/Sep/19

$$\mathrm{Applying}\mathrm{by}\mathrm{part}$$$$=\mathrm{x}.\ln (\mathrm{x}+4)-\int \frac{\mathrm{x}\mathrm{dx}}{\mathrm{x}+4}$$$$=\mathrm{xln}(\mathrm{x}+4)-[\int \mathrm{dx}-4\int \frac{\mathrm{dx}}{\mathrm{x}+4}]$$$$=\mathbf{xl}(\mathbf{x}+4)-\mathbf{x}+4\mathbf{ln}(\mathbf{x}+4)+\mathbf{c}$$$$\mathbf{please}\mathbf{check}.$$

Commented by Rio Michael last updated on 15/Sep/19

$$ithinkperfect,thankssir$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com