Category: Integration

Question Number 197239 by universe last updated on 10/Sep/23 Answered by mahdipoor last updated on 11/Sep/23 $$\stackrel{\frac{d}{dx}}{\Rightarrow }{xsin}^{n}x=(\frac{{xsin}^{n}x}{n}-\frac{(n-1){xsin}^{n-2}{cos}^{2}x}{n}-\frac{{sin}^{n-1}xcosx}{n})$$$$+\left(\frac{{sin}^{{n}−\mathrm{1}}…

Question Number 197190 by universe last updated on 10/Sep/23 $${\int }_0^1{}^3\sqrt{1-x^7}dx-{\underset{0}{\int }}^1{}^7\sqrt{1-x^3}dx=?$$ Commented by Frix last updated…

Question Number 197177 by Mathspace last updated on 09/Sep/23 $$find{\int }_0^{\frac{\pi }{2}}{ln}^2\left(cosx\right)dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 197060 by universe last updated on 07/Sep/23 $$\mathrm{Prove}\mathrm{that}$$$${\underset{0}{\int }}^{\frac{\pi }{2}}\frac{\ln (1+\alpha \sin t)}{\sin t}dt=\frac{{\pi }^2}{8}-\frac{1}{2}{\left(\arccos \alpha \right)}^2$$ Commented by universe last updated on 07/Sep/23 $${question}\:\mathrm{196950}…

Question Number 196983 by universe last updated on 05/Sep/23 Commented by Frix last updated on 06/Sep/23 $$\mathrm{I}{\mathrm{can}}^{\prime }\mathrm{t}\mathrm{solve}\mathrm{the}\mathrm{first}2\mathrm{but}\mathrm{wolframalpha}\mathrm{can}$$$$\left(\mathrm{C}\mathrm{is}\mathrm{the}\mathrm{Catalan}\mathrm{constant}\right)$$$$\mathrm{1}.\:{I}_{\mathrm{1}} =\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{x}^{\mathrm{3}} }{…}{dx}=\frac{\pi\left(−\mathrm{1440C}+\mathrm{1144}+\mathrm{15}\pi\left(−\mathrm{41}+\mathrm{20}\pi+\mathrm{24ln}\:\mathrm{2}\right)\right)}{\mathrm{3780}}…