Category: Integration

Question Number 77752 by abdomathmax last updated on 09/Jan/20 $$letf\left(\lambda \right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{sin(\lambda e^x+e^{-x})}{x^2+{\lambda }^2}dxwith\lambda ⩾0$$$$1)detdrmineaexplicitformoff\left(\lambda \right)$$$$2)calculate{f}^{{}^{\prime }}\left(\lambda \right)atformofintergralandfind$$$$itsvalue.$$…

Question Number 12201 by Nayon last updated on 16/Apr/17 $$\int \frac{1}{sin\left(x\right)}dx$$ Answered by ajfour last updated on 16/Apr/17 $$I=\int \frac{\left(\mathrm{cosec}x\right)(\mathrm{cosec}x+\cot x)}{\mathrm{cosec}x+\cot x}dx$$$$let\mathrm{cosec}x+\cot x=t$$$$\frac{{dt}}{{dx}}=\:−\left(\mathrm{cosec}\:{x}\right)\mathrm{cot}\:{x}−\mathrm{cosec}\:^{\mathrm{2}} {x}…

Question Number 77716 by aliesam last updated on 09/Jan/20 $$\int sin\left(x^4\right)dx$$ Commented by MJS last updated on 09/Jan/20 $$\mathrm{this}\mathrm{can}\mathrm{be}\mathrm{solved}\mathrm{using}\mathrm{the}\mathrm{incomplete}$$$$\mathrm{gamma}\mathrm{function}.{\mathrm{I}}^{\prime }\mathrm{ll}\mathrm{post}\mathrm{it}\mathrm{later}$$…

Question Number 143230 by qaz last updated on 11/Jun/21 $$\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}\frac{{\mathrm{x}}^{3\mathrm{n}+1}}{3\mathrm{n}+1}=?$$ Answered by mathmax by abdo last updated on 11/Jun/21 $$\mathrm{f}\left(\mathrm{x}\right)=\sum_{\mathrm{n}=\mathrm{o}}…

Question Number 12141 by tawa last updated on 14/Apr/17 $$\int \sin \left({\mathrm{x}}^4\right)\cos \left({\mathrm{x}}^2\right)\mathrm{dx}$$ Answered by geovane10math last updated on 15/Apr/17 $$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know},\mathrm{put}\mathrm{this}\mathrm{integral}\mathrm{in}\mathrm{the}$$$$\mathrm{Wolfram}\:\mathrm{Alpha}. \…