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Category: Integration

In-x-2-e-cos2-x-dx-

Question Number 164590 by Zaynal last updated on 19/Jan/22 $$\int\:\frac{\mathrm{In}\left(\mathrm{x}^{\mathrm{2}} .\boldsymbol{{e}}^{\boldsymbol{{cos}}\mathrm{2}} \right)}{\boldsymbol{\mathrm{x}}}\:\boldsymbol{\mathrm{dx}} \\ $$ Answered by mahdipoor last updated on 19/Jan/22 $$=\int\frac{{cos}\mathrm{2}+\mathrm{2}{lnx}}{{x}}{dx}={lnx}.{cos}\mathrm{2}+{ln}^{\mathrm{2}} {x}+{C} \\ $$…

2cos-x-3-cos-2x-dx-

Question Number 33507 by MJS last updated on 18/Apr/18 $$\int\frac{\mathrm{2cos}\:{x}}{\mathrm{3}−\mathrm{cos}\:\mathrm{2}{x}}{dx}=? \\ $$ Answered by math1967 last updated on 18/Apr/18 $$\int\frac{\mathrm{2}{cosx}}{\mathrm{3}−\mathrm{1}+\mathrm{2}{sin}^{\mathrm{2}} {x}}{dx} \\ $$$$\int\frac{\mathrm{2}{cosx}}{\mathrm{2}\left(\mathrm{1}+{sin}^{\mathrm{2}} {x}\right)}{dx} \\…

Let-I-y-2-2-y-3-cos-y-2-1-2-4-y-2-dy-then-I-y-

Question Number 99007 by Rio Michael last updated on 18/Jun/20 $$\mathrm{Let}\:{I}_{{y}} \:=\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\left[{y}^{\mathrm{3}} \:\mathrm{cos}\:\left(\frac{{y}}{\mathrm{2}}\right)\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right]\left(\sqrt{\mathrm{4}−{y}^{\mathrm{2}} }\:\right)\:{dy}\: \\ $$$$\mathrm{then}\:{I}_{{y}} \:=\:??? \\ $$ Answered by maths mind…

tan-1-5-x-cotx-secxdx-

Question Number 98951 by Dwaipayan Shikari last updated on 17/Jun/20 $$\int{tan}^{\frac{\mathrm{1}}{\mathrm{5}}} {x}.{cotx}.{secxdx} \\ $$ Commented by MJS last updated on 18/Jun/20 $$\mathrm{this}\:\mathrm{should}\:\mathrm{lead}\:\mathrm{to}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{including} \\ $$$$\mathrm{the}\:\mathrm{hyper}\:\mathrm{geometrical}\:\mathrm{function}\:_{\mathrm{2}} {F}_{\mathrm{1}}…

let-g-x-cosx-1-cos-2x-3-developp-f-at-fourier-serie-

Question Number 98944 by mathmax by abdo last updated on 17/Jun/20 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{cosx}\:+\mathrm{1}}{\mathrm{cos}\left(\mathrm{2x}\right)−\mathrm{3}}\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 18/Jun/20 $$\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{cosx}+\mathrm{1}}{\mathrm{cos}\left(\mathrm{2x}\right)−\mathrm{3}}\:=\frac{\frac{\mathrm{e}^{\mathrm{ix}} \:+\mathrm{e}^{−\mathrm{ix}}…

calculate-x-1-2x-3-x-2-x-1-dx-

Question Number 98942 by mathmax by abdo last updated on 17/Jun/20 $$\mathrm{calculate}\:\int\:\frac{\mathrm{x}+\mathrm{1}−\sqrt{\mathrm{2x}+\mathrm{3}}}{\mathrm{x}−\mathrm{2}\:+\sqrt{\mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$ Commented by MJS last updated on 17/Jun/20 $$\mathrm{Sir}\:\mathrm{Abdo},\:\mathrm{do}\:\mathrm{you}\:\mathrm{have}\:\mathrm{an}\:\mathrm{easy}\:\mathrm{solution}? \\ $$$$\mathrm{I}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{but}\:\mathrm{the}\:\mathrm{constants}\:\mathrm{are}\:\mathrm{getting} \\…