H.T.H

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5 Questions

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1	Showing that: $(\frac{a}{b+c})^2+(\frac{b}{a+c})^2+(\frac{c}{a+b})^2+\frac{10abc}{(a+b)(b+c)(c+a)}\ge 2$
1	$\sqrt{(a+b-c)(b+c-a)(c+a-b)} \le \frac{3\sqrt{3}abc}{(a+b+c)\sqrt{a+b+c}}$
1	Integrals: $I=\int_{1}^{e}\frac{\ln x(\ln x+1)}{(1+x+\ln x)^3}dx$
-2	$(\cot \alpha)^{\cos 2\alpha} \ge \frac{1}{\sin 2\alpha}$
-3	Solve the equations: $\log_{2}x=\log_{5-x}3$

58 Reputation

+3	Solve the equations: $\log_{2}x=\log_{5-x}3$
+5	$(\cot \alpha)^{\cos 2\alpha} \ge \frac{1}{\sin 2\alpha}$
+20	Integrals: $I=\int_{1}^{e}\frac{\ln x(\ln x+1)}{(1+x+\ln x)^3}dx$
+5	Integrals: $I=\int_{1}^{e}\frac{\ln x(\ln x+1)}{(1+x+\ln x)^3}dx$

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2 Answers

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2	Integrals: $I=\int_{1}^{e}\frac{\ln x(\ln x+1)}{(1+x+\ln x)^3}dx$
1	Showing that: $(\frac{a}{b+c})^2+(\frac{b}{a+c})^2+(\frac{c}{a+b})^2+\frac{10abc}{(a+b)(b+c)(c+a)}\ge 2$

6 Tags

2 integral × 2	0 logarithms
1 homework × 3	0 trigonometry
1 inequality × 3	0 geometry

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