Category: Integration

Question Number 37067 by math khazana by abdo last updated on 08/Jun/18 $$find\int \frac{dx}{(x+1)\sqrt{1+x^2}}$$ Commented by math khazana by abdo last updated on…

Question Number 37028 by nishant last updated on 08/Jun/18 $$\int \frac{2x-1}{5x^2-x+2}dx=?$$ Answered by ajfour last updated on 08/Jun/18 $$I=\frac{1}{5}\int \frac{10x-1}{5x^2-x+2}dx-\frac{4}{25}\int \frac{dx}{{(x-\frac{1}{10})}^2+\frac{2}{5}-\frac{1}{100}}$$$$\:\:=\frac{\mathrm{1}}{\mathrm{5}}\mathrm{ln}\:\mid\mathrm{5}{x}^{\mathrm{2}}…

Question Number 37018 by behi83417@gmail.com last updated on 08/Jun/18 Commented by math khazana by abdo last updated on 08/Jun/18 $$1)letI=\int \frac{\sqrt{1+x^2}}{1+x}dxchangementx=shtgive$$$${I}\:=\:\int\:\:\:\:\frac{{ch}\left({t}\right)}{\mathrm{1}+{sh}\left({t}\right)}{ch}\left({t}\right){dt}=\:\int\:\:\:\frac{{ch}^{\mathrm{2}} \left({t}\right){dt}}{\mathrm{1}+{sh}\left({t}\right)} \…

Question Number 36997 by rahul 19 last updated on 07/Jun/18 $$\int \sqrt{\frac{1+x}{x}}dx=?$$ Commented by behi83417@gmail.com last updated on 07/Jun/18 $$x={tg}^{2}t\Rightarrow dx=2tgt(1+{tg}^{2}t)dt$$$${I}=\int\sqrt{\frac{\mathrm{1}+{tg}^{\mathrm{2}}…

Question Number 36965 by MJS last updated on 07/Jun/18 $$\int \frac{x^5-x^4+x^3-1}{{(x^2-x+1)}^3}dx=$$ Commented by rahul 19 last updated on 07/Jun/18…