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Question Number 53502 by 0955083339 last updated on 22/Jan/19 $$\mathrm{If}(x-5)\mathrm{is}\mathrm{a}\mathrm{factor}\mathrm{of}2x^2+2px-2p=0,$$$$\mathrm{the}\mathrm{value}\mathrm{of}p\mathrm{is}$$ Answered by tanmay.chaudhury50@gmail.com last updated on 22/Jan/19 $$\mathrm{2}×\mathrm{5}^{\mathrm{2}} +\mathrm{2}{p}×\mathrm{5}−\mathrm{2}{p}=\mathrm{0} \…

Question Number 53386 by gunawan last updated on 21/Jan/19 $$\underset{0}{\stackrel{1}{\int }}\frac{dx}{e^x+e^{-x}}={\tan }^{-1}e-\frac{\pi }{4}$$ Commented by Tinkutara last updated on 21/Jan/19 $$=\int\frac{{e}^{{x}}…

Question Number 53383 by gunawan last updated on 21/Jan/19 $$\mathrm{If}\int \frac{1}{(\sin x+4)(\sin x-1)}dx$$$$=A\frac{1}{\tan \frac{x}{2}-1}+B{\tan }^{-1}\left(f\left(x\right)\right)+C,\mathrm{then}$$ Commented by maxmathsup by imad last updated on 21/Jan/19 $${let}\:{A}\:=\int\:\:\:\:\frac{{dx}}{\left({sinx}+\mathrm{4}\right)\left({sinx}−\mathrm{1}\right)}\:\Rightarrow{A}\:=_{{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}}…

Question Number 53381 by gunawan last updated on 21/Jan/19 $$\int \frac{1}{{\left[{(x-1)}^3{(x+2)}^5\right]}^{1/4}}dx=$$ Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jan/19 $$\int\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} \left({x}+\mathrm{2}\right)^{\frac{\mathrm{5}}{\mathrm{4}}} }…

Question Number 53359 by gunawan last updated on 20/Jan/19 $$\int \frac{x^3-1}{x^3+x}dx=$$ Answered by Smail last updated on 21/Jan/19 $${I}=\int\frac{{x}^{\mathrm{3}} +{x}−{x}−\mathrm{1}}{{x}^{\mathrm{3}} +{x}}{dx}=\int\left(\mathrm{1}−\frac{{x}+\mathrm{1}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\right){dx}…