Category: Integration

Question Number 190385 by TUN last updated on 02/Apr/23 Answered by mehdee42 last updated on 02/Apr/23 $$2\pi -x=u\Rightarrow dx=-du$$$$I={\int }_0^{2\pi }ln(-sinu+\sqrt{1+{sin}^{2}u})du$$$$=\int_{\mathrm{0}} ^{\mathrm{2}\pi}…

Question Number 124827 by mnjuly1970 last updated on 06/Dec/20 $$\dots .nicecalculus\dots$$$$provethat::$$$${\int }_0^{\frac{\pi }{2}}\frac{log(1+tan\left(x\right))}{tan\left(x\right)}dx=\frac{5{\pi }^2}{48}✓$$$$$$ Answered by mindispower last…

Question Number 124825 by Study last updated on 06/Dec/20 Commented by Study last updated on 07/Dec/20 $$pleasehelpme???$$ Commented by Study last updated on…

Question Number 59279 by Mr X pcx last updated on 07/May/19 $$find{\int }_0^{\frac{\pi }{2}}\frac{x}{sinx}dx$$ Commented by tanmay last updated on 07/May/19 $${f}\left({x}\right)=\frac{{x}}{{sinx}}\: \…

Question Number 59278 by Mr X pcx last updated on 07/May/19 $$letf\left(x\right)={\int }_0^{\mathrm{\infty }}\frac{ln(1+{xt}^2)}{2+t^2}dt$$$$determineaexplicitformoff\left(x\right)$$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt} \…