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Category: Integration

1-1-Inx-dx-

Question Number 201229 by Calculusboy last updated on 02/Dec/23 $$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\boldsymbol{{Inx}}}}\boldsymbol{{dx}} \\ $$ Commented by mnjuly1970 last updated on 02/Dec/23 $${In}\left({x}\right)\:{or}\:\:\mathrm{L}{n}\left({x}\right)=? \\ $$ Commented by Calculusboy…

1-1-sinx-dx-

Question Number 201224 by Calculusboy last updated on 02/Dec/23 $$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\boldsymbol{{sinx}}}}\boldsymbol{{dx}} \\ $$ Answered by witcher3 last updated on 02/Dec/23 $$\sqrt{\mathrm{1}+\mathrm{sin}\left(\mathrm{x}\right)}=\mathrm{hint}\::\mid\mathrm{sin}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)+\mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\mid \\ $$ Answered by Sutrisno…

x-4-x-7-1-4-x-2-dx-

Question Number 201227 by Calculusboy last updated on 02/Dec/23 $$\:\int\:\frac{\left(\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{x}}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}} \\ $$ Answered by Sutrisno last updated on 04/Dec/23 $$\:=\int\:\frac{\left(\boldsymbol{{x}}^{\mathrm{4}} \left(\mathrm{1}+\boldsymbol{{x}}^{\mathrm{3}}…

x-6-x-9-1-6-dx-

Question Number 201222 by Calculusboy last updated on 02/Dec/23 $$\:\int\:\left(\boldsymbol{{x}}^{\mathrm{6}} +\boldsymbol{{x}}^{\mathrm{9}} \right)^{\frac{\mathrm{1}}{\mathrm{6}}} \boldsymbol{{dx}} \\ $$ Answered by MathematicalUser2357 last updated on 04/Jan/24 $$\mathrm{A}\:\mathrm{function}\:\mathrm{that}\:\mathrm{contains}\:_{\mathrm{2}} {F}_{\mathrm{1}} \\…

1-1-x-dx-

Question Number 201223 by Calculusboy last updated on 02/Dec/23 $$\int\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\boldsymbol{{x}}}}\:\boldsymbol{{dx}} \\ $$ Answered by witcher3 last updated on 02/Dec/23 $$=\int\mathrm{2}\sqrt{\mathrm{1}+\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}}}.\frac{\mathrm{dx}}{\mathrm{2}\:\sqrt{\mathrm{1}+\mathrm{x}}} \\ $$$$=\mathrm{2}\int\sqrt{\mathrm{t}^{\mathrm{2}} +\mathrm{t}}\mathrm{dt} \\ $$$$\Leftrightarrow\int\mathrm{2}\sqrt{\left(\mathrm{t}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…