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Category: Integration

sin-x-4-dx-

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

dx-x-2-4x-1-

Question Number 143248 by cesarL last updated on 11/Jun/21 $$\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}} \\ $$ Commented by mohammad17 last updated on 11/Jun/21 $$ \\ $$$$=\int\:\frac{{dx}}{\left({x}−\mathrm{2}\right)^{\mathrm{2}} −\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{3}}\int\:\frac{−{dx}}{\mathrm{1}−\left(\frac{{x}−\mathrm{2}}{\:\sqrt{\mathrm{3}}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}{coth}^{−\mathrm{1}}…

n-1-x-3n-1-3n-1-

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

sin-x-4-cos-x-2-dx-

Question Number 12141 by tawa last updated on 14/Apr/17 $$\int\:\mathrm{sin}\left(\mathrm{x}^{\mathrm{4}} \right)\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{dx} \\ $$ Answered by geovane10math last updated on 15/Apr/17 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know},\:\mathrm{put}\:\mathrm{this}\:\mathrm{integral}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{Wolfram}\:\mathrm{Alpha}. \\…

Find-the-area-of-the-region-between-the-graphs-of-f-x-3x-3-x-2-10x-and-g-x-x-3-2x-

Question Number 12139 by tawa last updated on 14/Apr/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{between}\:\mathrm{the}\:\mathrm{graphs}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{3x}^{\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{10x} \\ $$$$\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:−\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{2x} \\ $$ Answered by mrW1 last updated on 15/Apr/17 $$\mathrm{3}{x}^{\mathrm{3}}…

a-x-a-x-a-x-a-x-

Question Number 12130 by sujith last updated on 14/Apr/17 $$\int\sqrt{{a}+{x}/{a}−{x}\:} \\ $$$$−\sqrt{{a}−{x}/{a}+{x}} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 14/Apr/17 $$\frac{{a}+{x}}{{a}−{x}}={t}^{\mathrm{2}} \Rightarrow\frac{{a}+{x}−{a}+{x}}{{a}+{x}+{a}−{x}}=\frac{{t}^{\mathrm{2}} −\mathrm{1}}{{t}^{\mathrm{2}} +\mathrm{1}}\Rightarrow{x}={a}\frac{{t}^{\mathrm{2}}…