Category: Integration

Question Number 49250 by cesar.marval.larez@gmail.com last updated on 04/Dec/18 $$Applyderivativecriteria$$$$F\left(x\right)=x^3+5x^2-2x+3$$ Answered by tanmay.chaudhury50@gmail.com last updated on 05/Dec/18 $$\frac{{dF}\left({x}\right)}{{dx}}=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{10}{x}−\mathrm{2}…

Question Number 49232 by Abdo msup. last updated on 04/Dec/18 $$letf\left(a\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}cos(x^2+ax+1)dx$$$$1)calculatef\left(a\right)and{f}^{{}^{\prime }}\left(a\right)$$$$2)find{f}^{\left(n\right)}\left(a\right)$$ Commented by Abdo…

Question Number 49187 by Rahul kharade last updated on 04/Dec/18 $$\int \frac{sinx}{sin4x}dx$$$$$$ Answered by MJS last updated on 04/Dec/18 $$\int \frac{\sin x}{\sin 4x}dx=$$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\rightarrow\:{dx}=\frac{\mathrm{2}{dt}}{{t}^{\mathrm{2}}…

Question Number 114681 by Dwaipayan Shikari last updated on 20/Sep/20 $$Provethat{\int }_0^{\mathrm{\infty }}\frac{x^n}{e^x-1}dx=n!\zeta (n+1)$$ Answered by mnjuly1970 last updated on 20/Sep/20 $$\:\:\:\:\:\:\:\:\:\:{proof}::…

Question Number 49134 by AdqhK ÐQeQqQ last updated on 03/Dec/18 $$\int \frac{1}{x^{1/6}+x^{1/3}}dx=??$$ Answered by arvinddayama01@gmail.com. last updated on 03/Dec/18 $$putx=t^6$$$$\:\:\:\:\:\:\:{dx}=\mathrm{6}{t}^{\mathrm{5}}…