Category: Integration

Question Number 20164 by tammi last updated on 23/Aug/17 $$\int \frac{e^{{\tan }^{-1}x}}{1+x^2}$$ Answered by ajfour last updated on 23/Aug/17 $${let}\:\mathrm{tan}^{−\mathrm{1}} {x}={t} \…

Question Number 20162 by ajfour last updated on 23/Aug/17 $$Computethevolumeofasolid$$$$boundedbyasurfacewithequation$$$${(x^2+y^2+z^2)}^2=a^{3}x.$$ Answered by ajfour last…

Question Number 20157 by ajfour last updated on 23/Aug/17 Commented by ajfour last updated on 23/Aug/17 $$Computethevolumecommontothe$$$$sphere{x}^2+y^2+z^2=4andtheinsideof$$$${the}\:{paraboloid}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…

Question Number 151221 by peter frank last updated on 19/Aug/21 $$\int \frac{\sin \mathrm{x}}{\sin (\mathrm{x}-\mathrm{a})}\mathrm{dx}$$ Commented by puissant last updated on 19/Aug/21 $$Q=\int \frac{sinx}{sin(x-a)}dx$$$$=\int \frac{sin(x-a+a)}{sin(x-a)}dx$$$$=\int\frac{{sin}\left({x}−{a}\right){cosa}+{cos}\left({x}−{a}\right){sina}}{{sin}\left({x}−{a}\right)}{dx}…

Question Number 85669 by john santu last updated on 23/Mar/20 $$\int \frac{\sqrt{1+x}}{\sqrt{1-x}}dx$$$$$$ Commented by mathmax by abdo last updated on 24/Mar/20 $${I}\:=\int\:\frac{\sqrt{\mathrm{1}+{x}}}{\:\sqrt{\mathrm{1}−{x}}}{dx}\:\Rightarrow\:{I}\:=\int\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}{dx}\:{we}\:{use}\:{the}\:{changement}\:…