List questions from substitution

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integrate $\sqrt{1^2 + 4t^2 + 9t^4 }$

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To prove $abc\leq\frac 18$

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Let $a,b,c$ be positive real numbers then prove the inequality $\frac{abc}{(a+1)(a+b)(b+c)(c+16)}≤\frac1{81}$

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Prove $\frac{x+1}{y+1}+\frac{y+1}{z+1}+\frac{z+1}{x+1}\leq\frac{x-1}{y-1}+\frac{y-1}{z-1}+\frac{z-1}{x-1}$

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List Question

How to get the same answer for integral $\int\frac{dz}{\sqrt{1+z^2}}$ as in textbook

How do I solve $\int\frac{\sqrt{x}}{\sqrt{x}-3}\,dx?$

Integration by substitution of a lineal function

How is this integral from $0\to\infty$ defined?

integrate $\sqrt{1^2 + 4t^2 + 9t^4 }$

find length of curve. how to parameterize a vector function when 0 <= t <= 1

Finding a solution for $yy'+xy=x^3 , \quad y=y(x)$

Substitution in the DE $y' \tan(y)+4x^3\cos(y)=2x$

Definite Integral $\int_{\frac{\pi}{12}}^{\frac{\pi}{4}}\frac{8\cos2x}{(\tan x+\cot x)^3}\,dx$.

Solving $\sqrt{-1+i}$

To prove $abc\leq\frac 18$

Let $a,b,c$ be positive real numbers then prove the inequality $\frac{abc}{(a+1)(a+b)(b+c)(c+16)}≤\frac1{81}$

If $ab+bc+ca+abc=4$, then $\sqrt{ab}+\sqrt{bc}+\sqrt{ca}\leq 3\leq a+b+c$

integrate $\int_{-1}^1 \frac{x}{2}\ln\frac{1+x}{1-x}\,dx=1$ between $-1$ and $1$.

Prove $\frac{x+1}{y+1}+\frac{y+1}{z+1}+\frac{z+1}{x+1}\leq\frac{x-1}{y-1}+\frac{y-1}{z-1}+\frac{z-1}{x-1}$

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