Category: Integration

Question Number 93098 by Rio Michael last updated on 10/May/20 $$\mathrm{find}\mathrm{the}\mathrm{general}\mathrm{solution}\mathrm{to}$$$$\int \frac{1}{a\sin x+b\cos x}dx\mathrm{and}\int \frac{1}{a\cos x-b\sin x}dx$$$$\mathrm{where}a,b\mathrm{are}\mathrm{constants}.$$$$$$ Commented by prakash jain last updated…

Question Number 158596 by mnjuly1970 last updated on 06/Nov/21 $$$$$$calculate:$$$$\mathrm{\Omega }={\int }_0^{\frac{\pi }{4}}\frac{1+{tan}^4\left(x\right)}{{cot}^2\left(x\right)}dx=?$$$$$$ Answered by puissant…

Question Number 158591 by cortano last updated on 06/Nov/21 $$I=\int \frac{dx}{1+x^6}=?$$ Commented by tounghoungko last updated on 06/Nov/21 $${I}=\int\:\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}\:{dx}−\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{6}} +\mathrm{1}}\:{dx}…

Question Number 93045 by john santu last updated on 10/May/20 $$\int {\sin }^{-1}\left(\sqrt{\frac{x}{2}}\right)dx$$ Commented by mathmax by abdo last updated on 10/May/20 $${I}\:=\int\:\:{arcsin}\left(\sqrt{\frac{{x}}{\mathrm{2}}}\right){dx}\:\:\:\:{changement}\:\sqrt{\frac{{x}}{\mathrm{2}}}={t}\:{give}\:\frac{{x}}{\mathrm{2}}={t}^{\mathrm{2}} \:\Rightarrow{x}=\mathrm{2}{t}^{\mathrm{2}}…

Question Number 27502 by abdo imad last updated on 07/Jan/18 $$find{\int }_0^{\frac{\pi }{2}}\frac{ln(1+{xsin}^{2}t)}{{sin}^{2}t}dtwith-1<x<1.$$ Commented by abdo imad last updated on 09/Jan/18…