Category: Integration

Question Number 68767 by aliesam last updated on 15/Sep/19 Commented by ~ À ® @ 237 ~ last updated on 15/Sep/19 $$Letnamedit{f}_n\left(x\right)$$$${Let}\:{named}\:\:\forall\:{a}>\mathrm{0}\:\:{g}\left({a},{x}\right)=\int\:\frac{{dx}}{{a}+{x}^{\mathrm{2}}…

Question Number 134289 by bramlexs22 last updated on 02/Mar/21 $$\mathrm{I}=\int \frac{{\mathrm{x}}^{\mathrm{n}}}{\sqrt{\mathrm{ax}+\mathrm{b}}}\mathrm{dx}$$$$\mathrm{H}=\int \frac{{\mathrm{x}}^4}{\sqrt{2\mathrm{x}+1}}\mathrm{dx}$$ Answered by EDWIN88 last updated on 02/Mar/21 $$\mathrm{I}_{\mathrm{n}} =\:\frac{\mathrm{2x}^{\mathrm{n}}…

Question Number 134272 by mnjuly1970 last updated on 01/Mar/21 $$\mathrm{nice}\mathrm{calculus}$$$$\mathrm{prove}\mathrm{that}::$$$$i::={\int }_0^{\mathrm{\infty }}\frac{cos\left(\pi x\right)}{e^{2\pi \sqrt{x}}-1}dx=\frac{2-\sqrt{2}}{8}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ii}::\:{compute}:\:\:\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{4}} +\mathrm{9}{n}^{\mathrm{2}} +\mathrm{10}}\:=? \…

Question Number 68699 by Rio Michael last updated on 15/Sep/19 $$\int ln(x+4)dx=$$ Commented by mathmax by abdo last updated on 15/Sep/19 $$letI=\int ln(x+4)dxchangementx+4=tgive$$$${I}\:=\int{lnt}\:{dt}\:={tln}\left({t}\right)−{t}\:+{c}\:=\left({x}+\mathrm{4}\right){ln}\left({x}+\mathrm{4}\right)−{x}−\mathrm{4}\:+{c}…

Question Number 134227 by Raxreedoroid last updated on 01/Mar/21 $$\mathrm{I}\mathrm{struck}\mathrm{upon}\mathrm{this}$$$$\underset{n=0}{\sum ^{\mathrm{\infty }}}{16}^n=\frac{-1}{15}$$$${\int }_0^{\pi }{\cos }^{4}x\sin xdx=\frac{-1}{5}{\left[{\cos }^{5}x\right]}_0^{\pi }=0.4$$$$\mathrm{in}\:\mathrm{another}\:\mathrm{way}…