Question Number 211344 by Nadirhashim last updated on 06/Sep/24 $$\:\:\:{find}\:\int\frac{\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{3}} \left(\boldsymbol{{x}}\right)\:\boldsymbol{{cos}}^{\mathrm{5}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\: \\ $$ Answered by Frix last updated on 06/Sep/24 $$\int\frac{{dx}}{\mathrm{cos}^{\mathrm{5}} \:{x}\:\mathrm{sin}^{\mathrm{3}} \:{x}}=\int\frac{\left(\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \:{x}\right)^{\mathrm{4}}…
Question Number 211245 by Ghisom last updated on 01/Sep/24 $$\mathrm{prove}: \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{t}^{\alpha−\mathrm{1}} }{{t}^{\pi} +\mathrm{1}}{dt}=\frac{\mathrm{1}}{\mathrm{sin}\:\alpha} \\ $$ Answered by Frix last updated on 02/Sep/24…
Question Number 211155 by Spillover last updated on 30/Aug/24 $$\int\frac{\left(\mathrm{sin}\:^{{n}} \left(\theta\right)−\mathrm{sin}\:\left(\theta\right)\right)^{\frac{\mathrm{1}}{{n}}} \mathrm{cos}\:\left(\theta\right)}{\mathrm{sin}\:^{{n}+\mathrm{1}} \left(\theta\right)}{d}\theta \\ $$$$ \\ $$ Answered by Frix last updated on 30/Aug/24 $$=\int\frac{{d}\theta}{\mathrm{sin}\:\theta}\:−\int\left(\mathrm{sin}\:\theta\right)^{\frac{\mathrm{1}−{n}−{n}^{\mathrm{2}}…
Question Number 211184 by nothing48 last updated on 30/Aug/24 Answered by mm1342 last updated on 30/Aug/24 $${x}={sinu} \\ $$$$\Rightarrow\int{sin}^{\mathrm{3}} {udu}=\int\left(\mathrm{1}−{cos}^{\mathrm{2}} {u}\right){sinudu} \\ $$$$=−{cosu}+\frac{\mathrm{1}}{\mathrm{3}}{cos}^{\mathrm{3}} {u}+{c} \\…
Question Number 211152 by Spillover last updated on 29/Aug/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\sqrt{{x}}}{\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} }{dx} \\ $$$$ \\ $$ Answered by Ghisom last updated…
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Question Number 211151 by Spillover last updated on 29/Aug/24 $$ \\ $$$$ \\ $$$$\int\frac{{dx}}{{x}\mathrm{ln}\:{x}\left(\mathrm{ln}\:\mathrm{ln}\:{x}−\mathrm{1}\right)\left(\mathrm{ln}\:\mathrm{ln}\:{x}−\mathrm{2}\right)\left(\mathrm{ln}\:\mathrm{ln}\:{x}−\mathrm{3}\right)\left(\mathrm{ln}\:\mathrm{ln}\:{x}−\mathrm{4}\right)} \\ $$$$ \\ $$$$ \\ $$ Answered by Ghisom last updated…
Question Number 211150 by Spillover last updated on 29/Aug/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\mathrm{tan}\:^{\mathrm{2}} \theta+\mathrm{tan}\:^{\mathrm{5}} \theta\right){e}^{\mathrm{tan}\:^{\mathrm{2}} \theta} {d}\theta \\ $$$$ \\ $$$$ \\ $$ Commented…
Question Number 211006 by universe last updated on 26/Aug/24 Answered by mr W last updated on 26/Aug/24 $$=\mathrm{0}\:{because}\:{of}\:{odd}\:{function}\:{zy}^{\mathrm{2}} \\ $$ Commented by mr W last…