Category: Integration

Question Number 91269 by mathmax by abdo last updated on 29/Apr/20 $$calculate{\int }_0^{\mathrm{\infty }}\frac{x^2-1}{{(x^2+x+2)}^3}dx$$ Terms of Service Privacy Policy Contact:…

Question Number 156775 by mnjuly1970 last updated on 15/Oct/21 $$$$$$fisafunctionthatassigns$$$$toeachnaturalnumber$$$$multiplicationofitsdigits$$$$forexampl:f\left(200\right)=0$$$$f\left(128\right)=1\times 2\times 8=16$$$$findthevalueof:$$$$\:\:\:\:\:{f}\:\left(\mathrm{100}\right)\:+\:{f}\left(\mathrm{101}\:\right)+\:{f}\:\left(\mathrm{102}\:\right)+…{f}\left(\mathrm{999}\right)=? \…

Question Number 156761 by gsk2684 last updated on 15/Oct/21 $$provethat$$$$\int \frac{a+b\sin x}{{(b+a\sin x)}^2}dx=\frac{-\cos x}{b+a\sin x}$$ Answered by cortano last updated on 15/Oct/21 $$\:\frac{\mathrm{d}}{\mathrm{dx}}\int\frac{\mathrm{a}+\mathrm{bsin}\:\mathrm{x}}{\left(\mathrm{b}+\mathrm{asin}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}=\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{−\mathrm{cos}\:\mathrm{x}}{\mathrm{b}+\mathrm{asin}\:\mathrm{x}}\right) \…

Question Number 25682 by abdo imad last updated on 13/Dec/17 $$wegive{\int }_0^{\mathrm{\infty }}{t}^{a-1}{(1+t)}^{-1}dt=\pi {\left(sin\left(\pi a\right)\right)}^{-1}with0<a<1findthevalueof{\int }_0^{\mathrm{\infty }}{(1+x^{16})}^{-1}dx$$ Answered by ajfour…

Question Number 91217 by mhmd last updated on 28/Apr/20 Commented by Prithwish Sen 1 last updated on 28/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{n}\pi} \mid\mathrm{cosx}\mid\mathrm{dx}\:=\:\boldsymbol{\mathrm{n}}\int_{\mathrm{0}} ^{\boldsymbol{\pi}} \mid\mathrm{cosx}\mid\mathrm{dx}\:=\:\mathrm{n}\left[\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{\mathrm{cosxdx}}+\int_{\frac{\boldsymbol{\pi}}{\mathrm{2}}}…