Category: Integration

Question Number 56829 by maxmathsup by imad last updated on 24/Mar/19 $$letf\left(t\right)={\int }_0^{\mathrm{\infty }}\frac{cos\left(t(1+x^2)\right)}{1+x^2}dxwitht⩾0$$$$findaexplicitformoff\left(t\right)$$ Answered by Smail last updated…

Question Number 187898 by cortano12 last updated on 23/Feb/23 $$\int \frac{1-\cos \mathrm{x}}{\cos \mathrm{x}+\sin \mathrm{x}-1}\mathrm{dx}=?$$ Answered by horsebrand11 last updated on 24/Feb/23 $$=\frac{1}{2}\int \frac{2-2\cos x}{\cos x+\sin -1}dx$$$$=\frac{1}{2}\int \frac{(1-\cos x+\sin x)-(\cos x+\sin x-1)}{\cos x+\sin x-1}dx$$$$=−\frac{\mathrm{1}}{\mathrm{2}}{x}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}{x}}{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{x}−\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}{x}}\:{dx} \…

Question Number 122349 by liberty last updated on 16/Nov/20 $$\mathrm{Find}\mathrm{the}\mathrm{polynomial}\mathrm{P}\left(\mathrm{x}\right)\mathrm{of}\mathrm{least}\mathrm{degree}$$$$\mathrm{that}\mathrm{has}\mathrm{a}\mathrm{maximum}\mathrm{equal}\mathrm{to}6\mathrm{at}\mathrm{x}=1$$$$\mathrm{and}\mathrm{minimum}\mathrm{equal}\mathrm{to}2\mathrm{at}\mathrm{x}=3.$$ Commented by benjo_mathlover last updated on 17/Nov/20 $${my}\:{answer}\::\: \…

Question Number 122323 by mathmax by abdo last updated on 15/Nov/20 $$\mathrm{calculate}{\mathrm{A}}_{\mathrm{n}}={\int }_0^{\mathrm{\infty }}\frac{\mathrm{dx}}{({\mathrm{x}}^2+1)({\mathrm{x}}^2+2)\dots .({\mathrm{x}}^2+\mathrm{n})}$$$$\mathrm{wth}\mathrm{n}\mathrm{integr}\mathrm{natural}\mathrm{and}\mathrm{n}⩾1$$ Commented by Dwaipayan…

Question Number 122298 by mnjuly1970 last updated on 15/Nov/20 $$\dots nicecalculus\dots$$$$provethat:$$$$\underset{n=1}{\sum ^{\mathrm{\infty }}}\left\{\frac{\zeta (2n+1)-1}{n+1}\right\}=-\gamma +ln\left(2\right)✓$$$$..m.n.1970..$$ Answered by mindispower last updated…