\(\int\dfrac{1}{\sqrt{5x}-\sqrt{3x}}dx\)

\(\int\left(x^2-1\right)^3dx\\ \int\left(2-x^2\right)^4dx\\ \int\left(\dfrac{x^2+2\sqrt[3]{x}}{x}\right)^2dx\)

\(a,V=\left(\dfrac{1.\left(\sqrt{x}-2\right)}{x-4}+\dfrac{\sqrt{x}+2}{x-4}\right).\dfrac{\sqrt{x}+2}{\sqrt{x}}\\ =\dfrac{\sqrt{x}-2+\sqrt{x}+2}{x-4}.\dfrac{\sqrt{x}+2}{\sqrt{x}}\\ =\dfrac{2\sqrt{x}}{x-4}.\dfrac{\sqrt{x}+2}{\sqrt{x}}\\ =\dfrac{2}{\sqrt{x}-2}\)

\(b.\dfrac{2}{\sqrt{x}-2}=\dfrac{1}{3}\\ \Leftrightarrow6=\sqrt{x}-2\\ \Leftrightarrow\sqrt{x}=8\\ \Leftrightarrow x=64\left(t/m\right)\)

\(đk:\left\{{}\begin{matrix}x\ne-\dfrac{1}{3}\\x\ne\dfrac{1}{3}\end{matrix}\right.\)

\(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\left(\dfrac{6x^2+10x}{1-6x+9x^2}\right)\\ =\left(\dfrac{3x\left(3x+1\right)+2x\left(1-3x\right)}{1-9x^2}\right)\times\left(\dfrac{\left(1-3x\right)^2}{6x^2+10x}\right)\\ =\left(\dfrac{9x^2+3x+2x-6x^2}{1-9x^2}\right)\times\left(\dfrac{\left(1-3x\right)^2}{2x\left(3x+5\right)}\right)\\ =\left(\dfrac{3x^2+5x}{\left(1-3x\right)\left(1+3x\right)}\right)\times\left(\dfrac{\left(1-3x\right)^2}{2\left(3x^2+5x\right)}\right)\\ =\dfrac{1-3x}{2.\left(1+3x\right)}\)

Vì trong kiến và côn trùng khác có chứa acid formic ( \(HCOOH\) ) và acid đó tác dụng Nước vôi (Base) => làm trung hòa acid => giảm đau, sưng , rộp 

a,

 \(\Delta ABC=\Delta PQR\\ \Rightarrow\widehat{A}=\widehat{P}=50^o\\ \widehat{B}=\widehat{Q}\)

Xét \(ABC\) có

\(\widehat{A}+\widehat{B}+\widehat{C}=180^o\)

\(\Rightarrow\widehat{B}+\widehat{C}=130^o\\ \Rightarrow\widehat{B}=130^o-\widehat{C}\)

\(\widehat{B}-\widehat{C}=50^o\\ \Rightarrow130^o-2\widehat{C}=50^o\\ \Rightarrow\widehat{C}-40^o\\ \Rightarrow\widehat{B}=90^o=\widehat{Q}\)

\(\Rightarrow PQR\) là tam giác vuông

b, \(\Delta ABC=\Delta PQR\\ \Rightarrow\left\{{}\begin{matrix}AC=PR\\AB=PQ\\BC=QR\end{matrix}\right.\)

háp pi niu dia