Category: Integration

Question Number 186800 by universe last updated on 10/Feb/23 $$\mathbf{show}\mathbf{that}$$$${\int }_0^{\mathrm{\infty }}\frac{{\mathbf{tan}}^{-1}\mathit{\alpha }\mathit{x}{\mathbf{tan}}^{-1}\mathit{\beta }\mathit{x}}{{\mathit{x}}^2}\mathit{d}\mathit{x}=\frac{\mathit{\pi }}{2}\log \left\{\frac{{(\mathit{\alpha }+\mathit{\beta })}^{\mathit{\alpha }+\mathit{\beta }}}{{\mathit{\alpha }}^{\mathit{\alpha }}{\mathit{\beta }}^{\mathit{\beta }}}\right\}$$ Terms of Service…

Question Number 55702 by ajfour last updated on 02/Mar/19 $$s={\int }_0^x\sqrt{1+{(3t^2+p)}^2}dt=?$$$$takep=1foraspecialcase.$$ Commented by rahul 19 last updated on…

Question Number 121224 by liberty last updated on 06/Nov/20 $$\int \cos {}^2\mathrm{x}\tan {}^3\mathrm{x}\mathrm{dx}$$ Answered by benjo_mathlover last updated on 06/Nov/20 $$\:\int\:\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=\:−\int\:\frac{\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\right)\:\mathrm{d}\left(\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{cos}\:\mathrm{x}} \…

Question Number 55672 by gunawan last updated on 01/Mar/19 $$\mathrm{The}\mathrm{value}\mathrm{of}\mathrm{complex}\mathrm{integral}$$$${\int }_{\mid z\mid =1}(z^2\sin \frac{1}{z}+\frac{1}{z^2}\sin z)dz\mathrm{is}\dots$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 186736 by Rupesh123 last updated on 09/Feb/23 Answered by Frix last updated on 09/Feb/23 $$\lfloor \frac{2^0}{3}\rfloor =0\Rightarrow$$$${A}_{\mathrm{2}{n}} =\underset{{i}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\lfloor\frac{\mathrm{2}^{{i}} }{\mathrm{3}}\rfloor=\underset{{i}=\mathrm{1}} {\overset{{n}}…