Category: Integration

Question Number 137177 by mnjuly1970 last updated on 30/Mar/21 $$\dots \dots advanced\dots .calculus\dots .$$$$\mathrm{\Phi }=\underset{k=1}{\sum ^{\mathrm{\infty }}}\frac{{\psi }^{\prime }\left(k\right)}{k}=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{a}{n^b}$$$$a,b=??\left(adaptedfrombrilliant\right)$$$$\dots \dots \dots \dots \dots .$$$$\:\:\:\:\:\:\:\psi\left({k}\right)\overset{??} {=}−\gamma+\int_{\mathrm{0}} ^{\:\mathrm{1}}…

Question Number 137171 by mnjuly1970 last updated on 30/Mar/21 Answered by Dwaipayan Shikari last updated on 30/Mar/21 $$log\left(2\right)=1+1(-\frac{1}{2})+1(-\frac{1}{2})(-\frac{2}{3})+\dots$$$$=\frac{1}{1+\frac{\frac{1}{2}}{1-\frac{1}{2}+\frac{\frac{2}{3}}{1-\frac{2}{3}+\frac{\frac{3}{4}}{1-\frac{3}{4}+..}}}}=\frac{1}{1+\frac{1}{1+\frac{2^2}{1+\frac{3^2}{1+\frac{4^2}{1+\dots }}}}}$$$$\frac{\mathrm{1}}{{log}\left(\mathrm{2}\right)}=\mathrm{1}+\frac{\mathrm{1}^{\mathrm{2}}…

Question Number 137155 by mnjuly1970 last updated on 30/Mar/21 $$\dots \dots nicecalculus\dots \dots$$$$evaluate::$$$$\mathit{\varphi }={\int }_0^{2\pi }\frac{1}{1+{cos}^4\left(x\right)}dx=???$$ Answered by Ar Brandon last updated…

Question Number 137141 by Ar Brandon last updated on 30/Mar/21 $${\int }_0^1\frac{{\mathrm{t}}^4{(1-\mathrm{t})}^4}{1+{\mathrm{t}}^2}\mathrm{dt}$$ Answered by Ar Brandon last updated on…

Question Number 137123 by bobhans last updated on 30/Mar/21 $${\int }_0^1\frac{\mathrm{x}}{1+{\mathrm{x}}^8}\mathrm{dx}=?$$ Commented by Ar Brandon last updated on 30/Mar/21 You're right, Sir. Greetings to you ! It's been quite a longtime since we last interracted. Haha ! Commented…