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Category: Integration

0-pi-x-2-cos-2-x-xsin-x-cos-x-1-1-xsin-x-2-dx-

Question Number 205248 by universe last updated on 13/Mar/24 $$\:\:\:\int_{\mathrm{0}} ^{\pi} \:\frac{{x}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \left({x}\right)−{x}\mathrm{sin}\left({x}\right)−\mathrm{cos}\left({x}\right)−\mathrm{1}}{\left(\mathrm{1}+{x}\mathrm{sin}\left({x}\right)\right)^{\mathrm{2}} }{dx} \\ $$ Answered by Berbere last updated on 13/Mar/24 $$\left(\frac{{f}\left({x}\right)}{\mathrm{1}+{xsin}\left({x}\right)}+{g}\left({x}\right)\right)^{'}…

Is-there-any-way-to-integrate-1-ln-x-dx-without-hitting-the-Gauss-error-function-or-e-t-2-and-e-t-2-

Question Number 204992 by Akira181 last updated on 05/Mar/24 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{integrate}: \\ $$$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{ln}\left({x}\right)}}\:{dx} \\ $$$$\mathrm{without}\:\mathrm{hitting}\:\mathrm{the}\:\mathrm{Gauss}\:\mathrm{error}\:\mathrm{function} \\ $$$$\mathrm{or}\:{e}^{{t}^{\mathrm{2}} } \:\mathrm{and}\:{e}^{−{t}^{\mathrm{2}} } \:? \\ $$ Answered by TonyCWX08…

Question-204921

Question Number 204921 by mathlove last updated on 02/Mar/24 Answered by Frix last updated on 02/Mar/24 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{dx}}{\:\sqrt{{x}+\mathrm{3}}+\sqrt{{x}+\mathrm{1}}}=\frac{\mathrm{1}}{\mathrm{2}}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{{x}+\mathrm{3}}−\sqrt{{x}+\mathrm{1}}{dx}= \\ $$$$=\left[\frac{\left({x}+\mathrm{3}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} −\left({x}+\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{\mathrm{3}}\right]_{\mathrm{0}}…

calculate-0-1-x-1-x-dx-

Question Number 204902 by pticantor last updated on 01/Mar/24 $$\boldsymbol{{calculate}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}\boldsymbol{{dx}} \\ $$ Answered by witcher3 last updated on 01/Mar/24 $$\mathrm{y}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} −\mathrm{x}=\mathrm{0}\Leftrightarrow\mathrm{y}^{\mathrm{2}} +\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…