Category: Integration

Question Number 142719 by gsk2684 last updated on 04/Jun/21 $$\mathrm{find}\mathrm{the}\mathrm{particular}\mathrm{solution}$$$$\mathrm{to}\mathrm{the}\mathrm{differential}\mathrm{equation}$$$${\mathrm{y}}^{\left(4\right)}+{21\mathrm{y}}^{\left(2\right)}-100\mathrm{y}=4(8-29\mathrm{t}){\mathrm{e}}^{-2\mathrm{t}}.$$$$\mathrm{solution}\mathrm{please}.$$ Commented by gsk2684 last…

Question Number 11621 by Nayon last updated on 29/Mar/17 $$Evaluate\int \frac{ax+b}{cx+d}dx$$ Answered by mrW1 last updated on 29/Mar/17 $$=\int \frac{\frac{a}{c}(cx+d)+(b-\frac{ad}{c})}{cx+d}dx$$$$=\frac{a}{c}\int dx+(b-\frac{ad}{c})\times \frac{1}{c}\int \frac{d(cx+d)}{cx+d}$$$$=\frac{{ax}}{{c}}+\frac{{bc}−{ad}}{{c}^{\mathrm{2}} }×\mathrm{ln}\:\left({cx}+{d}\right)+{C}…

Question Number 142689 by rs4089 last updated on 04/Jun/21 Answered by Dwaipayan Shikari last updated on 04/Jun/21 $${\int }_0^{\mathrm{\infty }}\frac{sin\left(x\right)}{x}f\left(x\right)dx={\int }_0^{\frac{\pi }{2}}f\left(x\right)dxf(x\pm \pi )=f\left(x\right)$$$${let}\:{f}\left({x}\right)={sin}^{\mathrm{2}{n}−\mathrm{2}} {x}\:\:\:\:\:\:…

Question Number 142687 by iloveisrael last updated on 04/Jun/21 $$\int \frac{dx}{\sqrt{1-\sin x}\sqrt{1+\cos x}}=?$$ Answered by qaz last updated on 04/Jun/21 $$\int \frac{\mathrm{dx}}{\sqrt{1-\sin \mathrm{x}}\sqrt{1+\cos \mathrm{x}}}$$$$=\frac{1}{\sqrt{2}}\int \frac{\mathrm{dx}}{(\sin \frac{\mathrm{x}}{2}-\cos \frac{\mathrm{x}}{2})\cos \frac{\mathrm{x}}{2}}$$$$=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\frac{\mathrm{dx}}{\mathrm{2sin}\:\frac{\mathrm{x}}{\mathrm{2}}\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}−\mathrm{cos}\:^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}…

Question Number 11609 by Nayon last updated on 29/Mar/17 $$$$$$$$$$Evaluate\int x^{x}dx$$ Commented by Nayon last updated on 29/Mar/17 $${pls}\:{ans}\:{mrw}\mathrm{1}…