Question Number 202388 by Calculusboy last updated on 25/Dec/23 $$\:\:\boldsymbol{{P}}\:\boldsymbol{{rove}}\:\boldsymbol{{that}}:\:\:\:\:\int\:\frac{\boldsymbol{{dx}}}{\boldsymbol{{b}}^{\mathrm{4}} +\mathrm{2}\boldsymbol{{ax}}^{\mathrm{2}} +\boldsymbol{{c}}}=\frac{\boldsymbol{{tan}}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{2}}\sqrt{\boldsymbol{{a}}}\boldsymbol{{x}}}{\:\sqrt{\boldsymbol{{c}}+\boldsymbol{{b}}^{\mathrm{4}} }}\right)}{\:\sqrt{\mathrm{2}}\sqrt{\boldsymbol{{a}}}\sqrt{\boldsymbol{{c}}+\boldsymbol{{b}}^{\mathrm{4}} }}+\boldsymbol{{C}} \\ $$$$\boldsymbol{{if}}\:\:\boldsymbol{{a}}\centerdot\left(\boldsymbol{{c}}+\boldsymbol{{b}}^{\mathrm{4}} \right)>\mathrm{0} \\ $$$$ \\ $$ Answered by witcher3…
Question Number 202167 by tri26112004 last updated on 22/Dec/23 $$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \underset{{x}} {\int}^{\mathrm{1}} {sin}\left({y}^{\mathrm{2}} \right){dydx}\:=\:¿ \\ $$ Answered by mnjuly1970 last updated on 22/Dec/23 $$\:{answer}:=\:{sin}^{\mathrm{2}}…
Question Number 202212 by Calculusboy last updated on 22/Dec/23 Commented by BOYQOBILOV last updated on 23/Dec/23 $$ \\ $$ Answered by shunmisaki007 last updated on…
Question Number 202125 by Calculusboy last updated on 21/Dec/23 $$\int\:\frac{\boldsymbol{{sin}}\left(\mathrm{3}\boldsymbol{{x}}\right)}{\mathrm{1}+\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$ Answered by Frix last updated on 21/Dec/23 $$\mathrm{Let}\:{s}=\mathrm{sin}\:{x} \\ $$$$\frac{\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{3}} \:{x}}=\frac{{s}\left(\mathrm{4}{s}^{\mathrm{2}} −\mathrm{3}\right)}{\left({s}+\mathrm{1}\right)\left({s}^{\mathrm{2}}…
Question Number 202127 by Calculusboy last updated on 21/Dec/23 Answered by qaz last updated on 21/Dec/23 $$\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \frac{{dx}}{\mathrm{1}+\mathrm{tan}^{\pi} \:{x}}=\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \frac{{dx}}{\mathrm{1}+\mathrm{cot}\:^{\pi} {x}}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \left(\frac{\mathrm{1}}{\mathrm{1}+\mathrm{tan}^{\pi}…
Question Number 201980 by Calculusboy last updated on 17/Dec/23 Answered by Sutrisno last updated on 18/Dec/23 $${misal}\:{x}^{\mathrm{2}} ={t} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{dx}=\frac{{dt}}{\mathrm{2}{x}} \\ $$$$=\int{x}.{x}^{\mathrm{2}} {cot}\left({x}^{\mathrm{2}} \right)\frac{{dt}}{\mathrm{2}{x}} \\…
Question Number 201982 by Calculusboy last updated on 17/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201925 by Calculusboy last updated on 15/Dec/23 Commented by Calculusboy last updated on 17/Dec/23 $$\boldsymbol{{thanks}}\:\boldsymbol{{sir}} \\ $$ Commented by Frix last updated on…
Question Number 201817 by Calculusboy last updated on 13/Dec/23 Answered by witcher3 last updated on 13/Dec/23 $$=\int\left(\mathrm{sin}\left(\mathrm{ln}\left(\mathrm{x}+\mathrm{1}\right)\right)\left(\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{1}\right)\right)^{\mathrm{2}} \mathrm{dx} \\ $$$$=\int\mathrm{sin}^{\mathrm{2}} \left(\mathrm{ln}\left(\mathrm{x}+\mathrm{1}\right)\right)\left(\mathrm{x}+\mathrm{2}−\mathrm{2}\sqrt{\mathrm{x}+\mathrm{1}}\right) \\ $$$$\mathrm{ln}\left(\sqrt{\mathrm{x}+\mathrm{1}}\right)=\mathrm{t} \\ $$$$\mathrm{x}+\mathrm{1}=\mathrm{e}^{\mathrm{2t}}…
Question Number 201727 by Spillover last updated on 11/Dec/23 $$\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} {e}^{\mathrm{sin}\:{x}^{{c}\mathrm{os}\:{x}^{\mathrm{tan}\:{x}^{\mathrm{cot}\:{x}^{\mathrm{sec}\:{x}^{\mathrm{cosec}\:{x}} } } } } } {dx} \\ $$ Answered by MathematicalUser2357 last updated…