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How do I integrate this? Problem(error) with integration

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lim t→∞ 1/ln(t^2+1/t^2)Integrate[(sin(5x))^2/x,{x,1,πt}] is 1/4 by using brute force calculation, but how can i easily solve this????...

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Proof that the function $f(z)$ is constant in a domain $D$

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When $Bbb Z_n$ is a domain or field, i.e. $ab equiv 0 Rightarrow aequiv 0,$ or $,bequiv 0pmod{! n}$ and forms of zero divisors....

...Suppose $,ab equiv 0 pmod n,$ and $,0< n $ (so $nmid ab,... ...we may assume $b in B$ since $A(B,b) = AB,$ via $Ab = (I,a)b ... ...: abequiv 0,$ for $,a,bnotequiv 0. $ Let $,k =,$ additive...

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Using complete graphs and a combinatorial proof, show $sum_{i=1}^{j}$ ${k_i}choose{2} $ $leq$ ${n}choose{2}$...

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What is wrong with this? (Euler's Identity)

...float variable from Python to Wolfram Kernel?... ...$endgroup$ – Dietrich Burde 25 mins ago - New Focus Styles &... ...- Why doesn't Israel withdraw from the territories occupied during...

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Let $Ain M_2(mathbb{Z})$ s.t. there is a positive integer $n$ satisfying $A^n=I_2$. Show that $A^{12}=I_2$....

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When is this rational function of exponentials actually rational-valued?

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Why is my approach incorrect (threshold for Dice roll)?

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Projective closure of an affine variety of homogeneous polynomials

...I know that, in general, to find the projective closure of an affine...