Category: Integration

Question Number 68470 by mathmax by abdo last updated on 11/Sep/19 $$findthevalueof{\int }_0^{\mathrm{\infty }}\frac{arctan\left(2x^2\right)}{x^2+4}dx$$ Commented by mathmax by abdo last updated…

Question Number 68434 by mhmd last updated on 10/Sep/19 Answered by mind is power last updated on 10/Sep/19 $${\int }_a^{b}f\left(x\right)dx={\int }_a^{b}f(a+\mathrm{b}-\mathrm{x})\mathrm{dx}$$$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{3sin}\left(\mathrm{x}\right)−\mathrm{2sin}^{\mathrm{2}}…

Question Number 133963 by bobhans last updated on 25/Feb/21 $$\mathcal{Y}=\int \frac{dx}{\sqrt[6]{1+x^6}}?$$ Answered by EDWIN88 last updated on 26/Feb/21 $$\mathbb{Y}=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}\:\sqrt[{\mathrm{6}}]{\mathrm{1}+\mathrm{x}^{−\mathrm{6}} }}\:=\:\int\:\frac{\mathrm{x}^{\mathrm{6}} }{\mathrm{x}^{\mathrm{7}} \:\sqrt[{\mathrm{6}}]{\mathrm{1}+\mathrm{x}^{−\mathrm{6}} }}\:\mathrm{dx}\:…

Question Number 133951 by liberty last updated on 25/Feb/21 $$\mathcal{V}=\int \ln (\mathrm{x}+\sqrt{1+{\mathrm{x}}^2})\mathrm{dx}$$ Answered by mathmax by abdo last updated on 25/Feb/21 $$\Phi\:=\int\:\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}=\mathrm{sht}\:\Rightarrow \…

Question Number 133943 by mnjuly1970 last updated on 25/Feb/21 $$\dots \dots .advancedcalculus\dots \dots$$$$provethat:$$$$\mathit{\varphi }={\int }_0^{\mathrm{\infty }}\frac{cos\left(x^2\right)-cos\left(x\right)}{x}dx=\frac{\gamma }{2}$$$$\gamma :euler-mascheroniconstant\dots$$ Terms of Service Privacy…