Category: Integration

Question Number 113198 by mnjuly1970 last updated on 11/Sep/20 $$\dots .calculus\dots .$$$$\mathcal{E}valuate:::$$$$$$$$\mathrm{I}:={\int }_0^1\frac{1}{\sqrt{x(x+1)(x+2)(x+3)+1}-3x}dx=???$$$$$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\:\: \…

Question Number 178712 by mnjuly1970 last updated on 20/Oct/22 Answered by mr W last updated on 20/Oct/22 $$\frac{1}{n}\left(\frac{1}{4n^2-1}\right)=\frac{1}{2n}(\frac{1}{2n-1}-\frac{1}{2n+1})$$$$=\frac{1}{2n-1}+\frac{1}{2n+1}-\frac{1}{n}$$$$$$$$\underset{{n}=\mathrm{1}}…

Question Number 178692 by peter frank last updated on 20/Oct/22 $$\int \frac{\tan \left(\ln x\right).\tan \left(\ln \frac{x}{2}\right).\tan \left(\ln 2\right)}{x}dx$$$$$$ Answered by mindispower last updated on 21/Oct/22 $$tg(ln\left(\frac{x}{2}\right)+ln\left(2\right))=tg\left(lnx\right)=\frac{tg(ln\left[\left(2\right)\right)+tgg\left(ln\left(\frac{x}{2}\right)\right)}{1-tg\left(ln\left(2\right)\right)tg\left(ln\left(\frac{x}{2}\right)\right)}$$$$\Leftrightarrow{tg}\left({ln}\left({x}\right)\right){tg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)\right){tgln}\mathrm{2}=−{tgln}\left(\mathrm{2}\right)−{tgln}\frac{{x}}{\mathrm{2}}…

Question Number 47595 by ajfour last updated on 12/Nov/18 Commented by ajfour last updated on 12/Nov/18 $$RegardingQ.47497\left(someanalysis\right)$$$$AlsoseediagramofQ.47599$$$$forpartofsolution\left(sectionA\right).$$ Commented by…

Question Number 113110 by gopikrishnan last updated on 11/Sep/20 $${\stackrel{1}{\int }}_0\sqrt{x(x-1)dx}$$ Commented by 1549442205PVT last updated on 11/Sep/20 $$\mathrm{The}\mathrm{function}\sqrt{\mathrm{x}(\mathrm{x}-1)}\mathrm{is}\mathrm{defined}\mathrm{on}$$$$\mathrm{set}\:\mathrm{X}=\left(−\infty,\mathrm{0}\right]\cup\left[\mathrm{1},+\infty\right)\:\mathrm{and}\:\mathrm{isn}'\mathrm{t} \…