Category: Integration

Question Number 216772 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 MrGaster last updated on 19/Feb/25 $$\:\int\frac{\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)\:}{\mathrm{1}−\boldsymbol{{sec}}^{\mathrm{4}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\:=\int\frac{\mathrm{tan}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}−\left(\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}}…

Question Number 216742 by Tawa11 last updated on 17/Feb/25 $$\frac{1}{2}{\int }_0^1\frac{\ln (\mathrm{a}-1)}{\mathrm{a}}\mathrm{da}$$ Answered by sniper237 last updated on 17/Feb/25 $$Notdefined!$$$${But}\:\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 216618 by Tawa11 last updated on 12/Feb/25 $${\int }_0^{2\pi }\sqrt{1-{\cos }^2\mathrm{x}}\mathrm{dx}$$$$\mathrm{Is}\mathrm{the}\mathrm{answer}0\mathrm{or}4????$$ Answered by A5T last updated on 12/Feb/25 $$\int_{\mathrm{0}}…

Question Number 216579 by MrGaster last updated on 11/Feb/25 $${\int }_0^{\frac{\pi }{4}}{\int }_0^{\frac{\pi }{4}}\frac{\tan (x^2+y^2)+\sin (x^2+y^2)}{\tan (x^2+y^2)+\cos (x^2+y^2)}dxdy$$ Terms…

Question Number 216486 by Tawa11 last updated on 08/Feb/25 $${\int }_0^1\mathrm{x}\sqrt{\mathrm{x}\sqrt[3]{\mathrm{x}\sqrt[4]{\mathrm{x}\sqrt[5]{\mathrm{x}\dots }}}}\mathrm{dx}$$ Answered by mehdee7396 last updated on 09/Feb/25 $${x}×{x}^{\frac{\mathrm{1}}{\mathrm{2}}} ×{x}^{\frac{\mathrm{1}}{\mathrm{6}}} ×{x}^{\frac{\mathrm{1}}{\mathrm{24}}} ×{x}^{\frac{\mathrm{1}}{\mathrm{120}}}…