Menu Close

Category: Integration

x-3x-3-2-dx-

Question Number 56523 by arvinddayama02@gmail.com last updated on 18/Mar/19 $$\int{x}\sqrt{\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}}\:{dx}=? \\ $$ Commented by MJS last updated on 18/Mar/19 $$\mathrm{it}\:\mathrm{seems}\:\mathrm{impossible}\:\mathrm{to}\:\mathrm{solve} \\ $$ Commented by…

nice-calculus-prove-that-0-1-ln-2-1-x-x-dx-3-4-m-n-

Question Number 122035 by mnjuly1970 last updated on 13/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)}{{x}}{dx}\overset{??} {=}\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}. \\ $$ Answered by mindispower…

x-2-sin-1-x-dx-

Question Number 187529 by sciencestudentW last updated on 18/Feb/23 $$\int{x}^{\mathrm{2}} \centerdot{sin}^{−\mathrm{1}} \left({x}\right){dx}=? \\ $$ Answered by Humble last updated on 18/Feb/23 $$\int\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{arcsin}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}} \\ $$$$\boldsymbol{{I}}{BP}…

9pi-2-7pi-1-5-dx-1-sinx-

Question Number 187528 by sciencestudentW last updated on 18/Feb/23 $$\underset{\frac{\mathrm{9}\pi}{\mathrm{2}}} {\overset{\frac{\mathrm{7}\pi}{\mathrm{1}.\mathrm{5}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{1}−{sinx}}}=? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23 $${I}=\int\frac{{dx}}{\:\sqrt{\mathrm{1}−\mathrm{sin}{x}}} \\ $$$$\:\:=\int\frac{{dx}}{\mid\mathrm{cos}\frac{{x}}{\mathrm{2}}−\mathrm{sin}\frac{{x}}{\mathrm{2}}\mid}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\frac{{dx}}{\mathrm{cos}\left(\frac{{x}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)} \\…

dx-cscx-1-

Question Number 187526 by sciencestudentW last updated on 18/Feb/23 $$\int\frac{{dx}}{{cscx}−\mathrm{1}}=? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23 $${I}=\int\frac{{dx}}{\mathrm{cosec}{x}−\mathrm{1}} \\ $$$$\:\:=\int\frac{\mathrm{sin}{x}}{\mathrm{1}−\mathrm{sin}{x}}{dx}=\int\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{sin}{x}}−\mathrm{1}\right){dx} \\ $$$$\:\:=\int\frac{\mathrm{1}+\mathrm{sin}{x}}{\mathrm{cos}^{\mathrm{2}} {x}}{dx}−{x}=\mathrm{tan}{x}+\frac{\mathrm{1}}{\mathrm{cos}{x}}−{x}+{C}…

4-9-n-x-x-dx-

Question Number 121965 by bemath last updated on 13/Nov/20 $$\:\:\:\:\:\underset{\mathrm{4}} {\overset{\mathrm{9}} {\int}}\:\frac{\ell{n}\:\left({x}\right)}{\:\sqrt{{x}}}\:{dx}\:? \\ $$ Answered by bemath last updated on 13/Nov/20 $$\:\underset{\mathrm{4}} {\overset{\mathrm{9}} {\int}}\:\frac{\ell{n}\left({x}\right)}{\:\sqrt{{x}}}\:{dx}\:=\:\underset{\mathrm{2}} {\overset{\mathrm{3}}…