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Category: Integration

0-2-4-x-x-x-4-x-dx-

Question Number 90784 by jagoll last updated on 26/Apr/20 $$\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:\sqrt{\frac{\mathrm{4}−{x}}{{x}}}−\sqrt{\frac{{x}}{\mathrm{4}−{x}}}\:{dx}\:? \\ $$ Commented by jagoll last updated on 26/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{2}} \:\frac{\left(\sqrt{\mathrm{4}−{x}}\right)^{\mathrm{2}} −\left(\sqrt{{x}}\right)^{\mathrm{2}}…

36-12cos-x-5sin-x-2-dx-

Question Number 156319 by cortano last updated on 10/Oct/21 $$\:\int\:\frac{\mathrm{36}}{\left(\mathrm{12cos}\:\mathrm{x}+\mathrm{5sin}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}=? \\ $$ Commented by john_santu last updated on 10/Oct/21 $$=\frac{\mathrm{36}}{\mathrm{13}}\left(\frac{\mathrm{12sin}\:{x}−\mathrm{5cos}\:{x}}{\mathrm{5sin}\:{x}+\mathrm{12cos}\:{x}}\right)+{c} \\ $$ Answered by…

sec-2-x-3sin-2-x-1-dx-

Question Number 156305 by cortano last updated on 10/Oct/21 $$\:\:\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{3sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{1}}\:\mathrm{dx} \\ $$ Answered by puissant last updated on 10/Oct/21 $$\Omega=\int\frac{{sec}^{\mathrm{2}} {x}}{\mathrm{3}{sin}^{\mathrm{2}} {x}−\mathrm{1}}{dx}\:=\:\int\frac{{sec}^{\mathrm{4}} {x}}{\mathrm{3}{tan}^{\mathrm{2}}…

if-ln-x-2-dx-x-ln-2-x-a-ln-x-b-C-a-b-C-are-constant-find-the-value-of-a-and-b-

Question Number 90765 by john santu last updated on 26/Apr/20 $${if}\:\int\:\left(\mathrm{ln}\left({x}\right)\right)^{\mathrm{2}} {dx}\:=\: \\ $$$${x}\left(\:\mathrm{ln}^{\mathrm{2}} \left({x}\right)+{a}\:\mathrm{ln}\left({x}\right)+{b}\right)\:+{C} \\ $$$${a},{b}\:,\:{C}\:{are}\:{constant}.\: \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}\: \\ $$ Commented by jagoll last…

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

Question Number 25224 by kshreyasingh200@gmil.com last updated on 06/Dec/17 $$\int\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{{x}×{x}−{x}+\mathrm{1}\:\:\:{dx}} \\ $$ Answered by prakash jain last updated on 06/Dec/17 $$\int\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:{dx} \\ $$$${x}^{\mathrm{2}} −{x}+\mathrm{1}={u}…

1-0-x-cos-t-ln-2-x-t-x-dt-dx-2-1-2-3-2-ln-x-dx-ln-pi-1-2-3-0-pi-2-cos-nt-cos-m-t-dt-pi-m-1-2-m-1-n-m-2-2-2-n-m-2-4-0-x-exp-pi

Question Number 90759 by  M±th+et+s last updated on 25/Apr/20 $$\mathrm{1}/\int_{\mathrm{0}} ^{\infty} \int_{{x}} ^{\infty} \frac{{cos}\left({t}\right)\:{ln}^{\mathrm{2}} \left({x}\right)}{{t}\sqrt{{x}}}{dt}\:{dx} \\ $$$$ \\ $$$$\mathrm{2}/\int_{\mathrm{1}/\mathrm{2}} ^{\mathrm{3}/\mathrm{2}} {ln}\left(\Gamma\left({x}\right)\right){dx}=\frac{{ln}\left(\pi\right)−\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{3}/\int_{\mathrm{0}}…