Question Number 133674 by liberty last updated on 23/Feb/21 $$\int\:\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{x}}}}\:\mathrm{dx}\:=?\: \\ $$ Answered by EDWIN88 last updated on 23/Feb/21 $$\:\mathrm{let}\:\mathrm{y}\:=\:\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{x}}}}\:\Rightarrow\sqrt{\mathrm{1}+\sqrt{\mathrm{x}}}\:=\:\mathrm{y}^{\mathrm{2}} −\mathrm{1} \\ $$$$\Rightarrow\mathrm{1}+\sqrt{\mathrm{x}}\:=\:\mathrm{y}^{\mathrm{4}} −\mathrm{2y}^{\mathrm{2}} +\mathrm{1}\:,\:\mathrm{x}\:=\:\left(\mathrm{y}^{\mathrm{4}}…
Question Number 68116 by aliesam last updated on 05/Sep/19 $$\int\frac{{dx}}{{sin}\mathrm{2}{x}−{sec}\left({x}\right)} \\ $$ Commented by MJS last updated on 06/Sep/19 $$\mathrm{look}\:\mathrm{at}\:\mathrm{question}\:\mathrm{68141} \\ $$ Answered by MJS…
Question Number 68100 by ~ À ® @ 237 ~ last updated on 04/Sep/19 $${Find}\:\:{K}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}−{t}+{t}^{\mathrm{2}} \right)}{{t}}\:{dt}\:\:\:\:\: \\ $$ Commented by mind is power…
Question Number 68094 by mhmd last updated on 04/Sep/19 $$\int{dx}/\sqrt[{{x}}]{\left(\pi+{e}\right)^{{x}^{\mathrm{2}} } }\: \\ $$ Answered by MJS last updated on 05/Sep/19 $$\int\frac{{dx}}{\:\sqrt[{{x}}]{\left(\pi+\mathrm{e}\right)^{{x}^{\mathrm{2}} } }}=\int\frac{{dx}}{\left(\pi+\mathrm{e}\right)^{{x}} }=−\frac{\mathrm{1}}{\left(\pi+\mathrm{e}\right)^{{x}}…
Question Number 68095 by mhmd last updated on 04/Sep/19 $$\int\sqrt{{x}}/\mathrm{1}+\sqrt[{\mathrm{3}}]{{x}\:}\:{dx} \\ $$ Answered by MJS last updated on 05/Sep/19 $$\int\frac{{x}^{\mathrm{1}/\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{1}/\mathrm{3}} }{dx}= \\ $$$$\:\:\:\:\:\left[{t}={x}^{\mathrm{1}/\mathrm{6}} \:\rightarrow\:{dx}=\mathrm{6}{x}^{\mathrm{5}/\mathrm{6}}…
Question Number 2526 by Filup last updated on 22/Nov/15 $$\mathrm{Evaluate}:\:\underset{−\infty} {\overset{\infty} {\int}}{e}^{−{x}^{\mathrm{2}} } {dx} \\ $$$$\mathrm{Please}\:\mathrm{show}\:\mathrm{and}\:\mathrm{explain}\:\mathrm{working} \\ $$ Commented by Filup last updated on 22/Nov/15…
Question Number 133591 by benjo_mathlover last updated on 23/Feb/21 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{x}^{\mathrm{2}} \:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:?\: \\ $$ Answered by EDWIN88 last updated on 23/Feb/21 $$\mathrm{by}\:\mathrm{Ostrogradsky}\:\mathrm{method} \\…
Question Number 68046 by mhmd last updated on 03/Sep/19 Answered by mind is power last updated on 03/Sep/19 $$\frac{{d}\left({e}^{\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} \right)}{{dx}}={cos}\left(\mathrm{2}{x}\right){e}^{{sin}\left({x}\right){cos}\left({x}\right)} \\ $$$$\int\frac{{e}^{{sin}\left({x}\right){cos}\left({x}\right)} {cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{e}^{{sin}\left(\mathrm{2}{x}\right)} }{dx} \\…
Question Number 68043 by mhmd last updated on 03/Sep/19 $$\int_{\pi/\mathrm{2}} ^{\pi} {e}^{{cosx}} \sqrt{\mathrm{1}−{e}^{{cosx}} }\:{sinx}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 03/Sep/19…
Question Number 68040 by mathmax by abdo last updated on 03/Sep/19 $${find}\:{f}\left({a}\right)\:=\int_{\mathrm{1}} ^{\mathrm{2}} {arctan}\left({x}+\frac{{a}}{{x}}\right){dx}\:\:{and} \\ $$$${calculate}\:{f}^{'} \left({a}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$ Commented by mathmax by abdo last…