Category: Integration

Question Number 147487 by mnjuly1970 last updated on 21/Jul/21 $$$$$$$$$$(a,2a+1]\cap [a^2-a,a^2+4a+1)\ne \varnothing$$$$$$$$a\in ?$$$$$$ Answered…

Question Number 81921 by M±th+et£s last updated on 16/Feb/20 Answered by MJS last updated on 16/Feb/20 $$\int \frac{\sqrt{\sqrt{x}+\sqrt{x-1}}}{\sqrt{x}+1}dx=$$$$[t=\sqrt{x}+\sqrt{x-1}\to dx=\frac{t^4-1}{2t^3}dt]$$$$=\int\frac{\left({t}−\mathrm{1}\right)\left({t}^{\mathrm{2}} +\mathrm{1}\right)}{\:\sqrt{{t}^{\mathrm{3}} }\left({t}+\mathrm{1}\right)}{dt}=…

Question Number 81888 by rajesh4661kumar@gmail.com last updated on 16/Feb/20 Commented by mathmax by abdo last updated on 16/Feb/20 $$letA=\int \frac{dx}{(x^2+1)\sqrt{x^2-1}}wedothechangementx=cht\Rightarrow$$$${A}\:=\int\:\:\:\frac{{sht}\:{dt}}{\left({ch}^{\mathrm{2}} {t}\:+\mathrm{1}\right){sht}}\:=\int\:\:\frac{{dt}}{\mathrm{1}+\frac{\mathrm{1}+{ch}\left(\mathrm{2}{t}\right)}{\mathrm{2}}}\:=\int\:\:\frac{\mathrm{2}{dt}}{\mathrm{3}+{ch}\left(\mathrm{2}{t}\right)} \…

Question Number 81801 by Power last updated on 15/Feb/20 Commented by mathmax by abdo last updated on 16/Feb/20 $$changement{x}^n={cos}^{2}tgivex={\left(cost\right)}^{\frac{2}{n}}\Rightarrow dx=-\frac{2}{n}sint{\left(cost\right)}^{\frac{2}{n}-1}$$$$\Rightarrow\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 16240 by tawa tawa last updated on 19/Jun/17 Commented by tawa tawa last updated on 19/Jun/17 $$\mathrm{please}\mathrm{help}.$$ Answered by ajfour last…