Category: Integration

Question Number 59344 by rahul 19 last updated on 08/May/19 $$\int e^x\left(\frac{1-\sin x}{1-\cos x}\right)dx=?$$ Answered by MJS last updated on 08/May/19 $$\mathrm{the}\mathrm{trick}\mathrm{is}\mathrm{this}:$$$$\frac{\mathrm{1}−\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}=\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:{x}}−\frac{\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}=\frac{\mathrm{1}}{\mathrm{2sin}^{\mathrm{2}} \:\frac{{x}}{\mathrm{2}}}−\frac{\mathrm{1}}{\mathrm{tan}\:\frac{{x}}{\mathrm{2}}}=…

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}}\: \…