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Category: Integration

dx-asin-x-bcos-x-

Question Number 152115 by peter frank last updated on 25/Aug/21 $$\int\frac{\mathrm{dx}}{\mathrm{asin}\:\mathrm{x}+\mathrm{bcos}\:\mathrm{x}} \\ $$ Answered by aleks041103 last updated on 26/Aug/21 $$\int\frac{\mathrm{dx}}{\mathrm{asin}\:\mathrm{x}+\mathrm{bcos}\:\mathrm{x}}= \\ $$$$=\frac{\mathrm{1}}{\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}\int\frac{{dx}}{{sin}\left({x}+{r}\right)},\:{r}={atan}\left({b}/{a}\right)…

tan-1-sec-x-tan-x-dx-

Question Number 152111 by peter frank last updated on 25/Aug/21 $$\int\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by peter frank last updated on 26/Aug/21 $$\int\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}}\right) \\…

0-1-x-1-1-x-1-dx-

Question Number 152105 by talminator2856791 last updated on 25/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{1}}{\lfloor{x}+\mathrm{1}\rfloor}\:−\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:{dx} \\ $$$$\: \\ $$ Answered by Olaf_Thorendsen last updated on 25/Aug/21…

Question-152094

Question Number 152094 by mnjuly1970 last updated on 25/Aug/21 Answered by Olaf_Thorendsen last updated on 25/Aug/21 $$\mathrm{7cos}{x}+\mathrm{4sin}{x}+\mathrm{5}\:=\:\mathrm{0}\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\mathrm{Let}\:{t}\:=\:\mathrm{tan}\frac{{x}}{\mathrm{2}} \\ $$$$\left(\mathrm{1}\right)\::\:\mathrm{7}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{4}\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{5}\:=\:\mathrm{0} \\…

dx-e-2x-5e-x-

Question Number 86518 by john santu last updated on 29/Mar/20 $$\int\:\:\frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{5e}^{\mathrm{x}} } \\ $$ Commented by john santu last updated on 29/Mar/20 $$\Rightarrow\:\int\:\:\frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{x}} \:\left(\mathrm{e}^{\mathrm{x}}…

x-2-1-x-4-1-dx-

Question Number 86491 by john santu last updated on 29/Mar/20 $$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}\:\mathrm{dx}\:?\: \\ $$ Commented by john santu last updated on 29/Mar/20 $$\mathrm{dear}\:\mathrm{prof}\:\mathrm{mr}\:\mathrm{mjs}.\:\mathrm{what}\:\mathrm{the}\:\mathrm{super} \\…