Category: Integration

Question Number 162365 by mathlove last updated on 29/Dec/21 $$\underset{0}{\stackrel{1}{\int }}\underset{0}{\stackrel{1}{\int }}\underset{0}{\stackrel{1}{\int }}{ln}^2(x+y+z)dxdydz=?$$ Terms of Service Privacy Policy Contact:…

Question Number 96784 by 175 last updated on 04/Jun/20 Answered by Sourav mridha last updated on 04/Jun/20 $$=\int \frac{2+{\mathit{x}}^2+\mathit{x}}{{\mathit{x}}^2\sqrt{{\mathit{x}}^2+\mathit{x}+1}}\mathit{d}\mathit{x}+\frac{2}{\mathit{x}}$$$$=\int\frac{\boldsymbol{{d}}\left(\boldsymbol{{x}}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\:\sqrt{\left(\boldsymbol{{x}}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{\mathrm{2}} }}+\frac{\mathrm{2}}{\boldsymbol{{x}}}…

Question Number 96771 by abdomathmax last updated on 04/Jun/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}-{\mathrm{y}}^{{}^{\prime }}+\mathrm{y}=\cos \left(2\mathrm{t}\right)\mathrm{with}\mathrm{y}\left(0\right)={\mathrm{y}}^{{}^{\prime }}\left(0\right)=-1$$ Answered by mathmax by abdo last updated on 05/Jun/20 $$\mathrm{let}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{laplce}\:…

Question Number 162297 by mathmax by abdo last updated on 28/Dec/21 $$\mathrm{find}{\int }_0^1\ln (1-\mathrm{x})\ln (1+\mathrm{x})\mathrm{dx}$$ Answered by Lordose last updated on 28/Dec/21 $$ \…

Question Number 96763 by bobhans last updated on 04/Jun/20 $$\int \frac{\sin \left(\frac{\mathrm{x}}{2}\right)\tan \left(\frac{\mathrm{x}}{2}\right)\mathrm{dx}}{\cos \mathrm{x}}=?$$ Answered by Sourav mridha last updated on 04/Jun/20 $$=\int \frac{1-\mathit{c}\mathit{o}\mathit{s}\mathit{x}}{2\mathit{c}\mathit{o}\mathit{s}\left(\frac{\mathit{x}}{2}\right)\mathit{c}\mathit{o}\mathit{s}\mathit{x}}\mathit{d}\mathit{x}$$$$=\int\frac{\boldsymbol{{sec}}^{\mathrm{2}} \frac{\boldsymbol{{x}}}{\mathrm{2}}}{\:\sqrt{\mathrm{1}−\boldsymbol{{tan}}^{\mathrm{2}} \frac{\boldsymbol{{x}}}{\mathrm{2}}}}\boldsymbol{{d}}\left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)−\int\boldsymbol{{sec}}\frac{\boldsymbol{{x}}}{\mathrm{2}}\boldsymbol{{d}}\left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)…