Category: Integration

Question Number 217122 by efronzo1 last updated on 01/Mar/25 $$\int \frac{\sqrt{\cos 2\mathrm{x}}}{\cos \mathrm{x}}\mathrm{dx}=?$$ Answered by Frix last updated on 01/Mar/25 $$\int \frac{\sqrt{\cos 2x}}{\cos x}dx=\int \frac{\sqrt{-1+{2\cos }^{2}x}}{\cos x}dx\stackrel{[t=\sqrt{2}\sin x]}{=}$$$$=\sqrt{\mathrm{2}}\int\frac{\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{\mathrm{2}−{t}^{\mathrm{2}}…

Question Number 216886 by Engr_Jidda last updated on 23/Feb/25 $${Evaluate}\:\frac{\underset{{k}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\int_{\mathrm{0}} ^{{k}} \left(\mathrm{4}{u}+\mathrm{1}\right){du}\right)}{\mathrm{5}^{\mathrm{2}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left(\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{2}}{{m}^{\mathrm{2}} +\mathrm{2}{m}}\right)^{{n}−\mathrm{1}} }\int_{{sin}^{−\mathrm{1}} \left(\frac{−\sqrt{\mathrm{2}}}{\mathrm{2}}\right)} ^{\frac{\pi}{\mathrm{2}}{cos}\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}−{sec}\theta{sin}\theta}{\frac{{tan}\theta+{cot}\theta}{\varrho^{\theta} −\varrho^{\pi{i}}…

Question Number 216799 by OPAVdx last updated on 20/Feb/25 Commented by MathematicalUser2357 last updated on 22/Feb/25 $$sen?$$ Answered by MATHEMATICSAM last updated on…

Question Number 216774 by Nadirhashim last updated on 19/Feb/25 $$\mathit{f}\mathit{i}\mathit{n}\mathit{d}\int \frac{{\mathit{t}\mathit{a}\mathit{n}}^2\left(\mathit{x}\right)}{1+{\mathit{s}\mathit{e}\mathit{c}}^4\left(\mathit{x}\right)}.\mathit{d}\mathit{x}$$ Answered by MathematicalUser2357 last updated on 25/Feb/25 $$\frac{\mathrm{1}}{\mathrm{2}}\left\{−\mathrm{2}{x}+\sqrt{\mathrm{1}−{i}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{tan}\left({x}\right)}{\:\sqrt{\mathrm{1}−{i}}}\right)+\sqrt{\mathrm{1}+{i}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{tan}\left({x}\right)}{\:\sqrt{\mathrm{1}+{i}}}\right)\right\}+{C} \…

Question Number 216754 by Tawa11 last updated on 17/Feb/25 $${\int }_0^1\frac{\mathrm{x}{\ln }^2\left(\mathrm{x}\right)}{1+{\mathrm{x}}^2}\mathrm{dx}$$ Answered by issac last updated on 18/Feb/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}}…