Category: Integration

Question Number 81279 by jagoll last updated on 11/Feb/20 $$\int \frac{\sqrt{2x+1}}{3x}dx=?$$ Commented by john santu last updated on 11/Feb/20 $$let{u}^2=2x+1\Rightarrow x=\frac{u^2-1}{2}$$$$\Rightarrow\frac{\mathrm{2}}{\mathrm{3}}\int\:\:\frac{{u}.\:{udu}}{{u}^{\mathrm{2}}…

Question Number 146791 by puissant last updated on 15/Jul/21 $$\int \frac{\mathrm{x}}{1+{\cos }^2\left(\mathrm{x}\right)}\mathrm{dx}$$ Answered by Ar Brandon last updated on 15/Jul/21 $$\mathrm{I}=\int\frac{\mathrm{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}=\int\frac{\mathrm{xsec}^{\mathrm{2}} \mathrm{x}}{\mathrm{sec}^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\mathrm{dx}…

Question Number 146756 by Bens last updated on 15/Jul/21 $$$$$$$$$$\underset{0}{\stackrel{1}{\int }}{t}^2+1dt$$ Answered by tabata last updated on…

Question Number 146736 by mnjuly1970 last updated on 15/Jul/21 $$$$$$1:\mathrm{S}:=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{n-1}}{n.2^n}=?$$$$2:\mathrm{A}:=\mathrm{\Sigma }\frac{{(-1)}^{n-1}}{n^2.2^n}=?$$ Answered by…

Question Number 146735 by qaz last updated on 15/Jul/21 $$\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}\frac{1+\frac{1}{2}+\frac{1}{3}+\dots +\frac{1}{\mathrm{n}}}{(\mathrm{n}+1)(\mathrm{n}+2)}=?$$ Answered by Olaf_Thorendsen last updated on 15/Jul/21 $$\mathrm{S}_{\mathrm{N}} \:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{N}} {\sum}}\frac{{H}_{{n}}…