Category: Integration

Question Number 122572 by rs4089 last updated on 18/Nov/20 Answered by Olaf last updated on 18/Nov/20 $$\mathrm{With}{\mathrm{Euler}}^{\prime }\mathrm{s}\mathrm{Gamma}\mathrm{function}\mathrm{\Gamma }:$$$${\int }_0^{\mathrm{\infty }}{e}^{-x}\ln xdx={\mathrm{\Gamma }}^{\prime }\left(1\right)=-\gamma$$$$\mathrm{where}\:\gamma\:\mathrm{is}\:\mathrm{the}\:\mathrm{Euler}−\mathrm{Mascheroni} \…

Question Number 122544 by bramlexs22 last updated on 18/Nov/20 $$anyonecanexplainmeabout$$$$Fresnelintegral?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 122528 by mnjuly1970 last updated on 17/Nov/20 $$\dots nicecalculus\dots$$$$\mathrm{\Omega }={\int }_0^{\frac{\pi }{2}}xsin\left(x\right).cos\left(x\right)ln(sin\left(x\right).ln\left(cos\left(x\right)\right)dx$$$$\stackrel{???}{=}\frac{\pi }{16}-\frac{{\pi }^3}{192}✓$$ Answered by mindispower last updated…

Question Number 188036 by Michaelfaraday last updated on 25/Feb/23 $$\int 2^x{e}^{x}dx$$ Answered by MJS_new last updated on 25/Feb/23 $$\int\mathrm{2}^{{x}} \mathrm{e}^{{x}} {dx}=\int\mathrm{e}^{\left(\mathrm{1}+\mathrm{ln}\:\mathrm{2}\right){x}} {dx}=\frac{\mathrm{e}^{\left(\mathrm{1}+\mathrm{ln}\:\mathrm{2}\right){x}}…

Question Number 188035 by Michaelfaraday last updated on 25/Feb/23 $$solve$$$$\int \frac{x^2}{{(a+bx)}^2}dx$$ Answered by MJS_new last updated on 25/Feb/23 $$\int\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}\right)^{\mathrm{2}}…