Category: Integration

Question Number 128346 by Ahmed1hamouda last updated on 06/Jan/21 Answered by MJS_new last updated on 06/Jan/21 $$\int x^2\sqrt{4x^2+1}dx=$$$$\:\:\:\:\:\left[{t}=\mathrm{2}{x}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}\:\rightarrow\:{dx}=\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}}{\mathrm{2}\left(\mathrm{2}{x}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}\right)}{dt}\right] \…

Question Number 62808 by mathmax by abdo last updated on 25/Jun/19 $$f\left(t\right)={\int }_0^{+\mathrm{\infty }}\frac{e^{-xt}}{{(x+t)}^2}dxwitht⩾0$$$$1)studythesetofdefinitionforf\left(t\right)$$$$2)studythecontinuityoff$$$$3)studythederivabilityoff$$$$\left.\mathrm{4}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \…

Question Number 128334 by liberty last updated on 06/Jan/21 $$\mathrm{\Omega }=\int \frac{{\mathrm{x}}^2}{\sqrt{{(\mathrm{a}+{\mathrm{bx}}^2)}^5}}\mathrm{dx};\mathrm{where}:\mathrm{a};\mathrm{b}>0$$ Answered by bramlexs22 last updated on 06/Jan/21 $$\Omega\:=\:\int\:\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}}…

Question Number 128316 by mnjuly1970 last updated on 08/Jan/21 $$nicecalculus$$$$\mathrm{\Omega }={\int }_0^{\mathrm{\infty }}\frac{{sin}^3\left(x\right)}{x^2}dx=?$$$$$$ Answered by mindispower last updated…

Question Number 128285 by john_santu last updated on 06/Jan/21 $$\cos \left(\frac{\pi }{7}\right)-\cos \left(\frac{2\pi }{7}\right)+\cos \left(\frac{3\pi }{7}\right)=?$$ Answered by liberty last updated on 06/Jan/21 $$\mathrm{let}\phi =\cos \left(\frac{\pi }{7}\right)-\cos \left(\frac{2\pi }{7}\right)+\cos \left(\frac{3\pi }{7}\right)$$$$\phi =\cos \left(\frac{\pi }{7}\right)+\cos \left(\frac{3\pi }{7}\right)+\cos \left(\frac{5\pi }{7}\right)$$$$\:\Rightarrow\mathrm{2}\varphi\mathrm{sin}\:\mathrm{t}\:=\:\mathrm{2sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:+\:\mathrm{2sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{3t}+\mathrm{2sin}\:\mathrm{tcos}\:\mathrm{5t} \…