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Dhanvin
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A 15 year old who likes Integrals and Number theory.

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9
Evaluating $\int_0^\infty \frac{\arctan (x^2) \ln(1+x^4)}{x(x^8+x^4+1)} \mathrm dx$
Jun 6, 2022
7
Prove that $\displaystyle\int_{0}^{\frac{1}{\sqrt{3}}}\frac{\arctan\left(\frac{1}{\sqrt{1-2x^2}}\right)}{1+x^2} \mathrm{dx}=\frac{13\pi^2}{288}$
Feb 3, 2022
7
How do you evaluate: $\int _{0}^{\infty} \frac{\log x}{e^x+e^{-x}+1} \ \mathrm dx$
Mar 19, 2022
6
Finding $\sum_{n=1}^{\infty}\frac{(-1)^n (H_{2n}-H_{n})}{n2^n \binom{2n}{n}}$
Apr 7, 2022
6
If $L=\lim_{m\to \infty}\sum_{p=1}^m \frac{p}{2p+m+m^2}$, then find floor(L).
Jun 17, 2022
5
Finding the solution of: $5^m -m^n=mn$
Mar 17, 2022
4
Prove $\left(\frac{a-b}{a+b}\right)^{11}+\left(\frac{b-c}{b+c}\right)^{11}+\left(\frac{c-a}{c+a}\right)^{11}\leq 1$ where $a,b,c >0$
Feb 13, 2022
4
Finding $\displaystyle \sum \limits _{n=1}^{\infty}\frac{(-1)^n (H_{2n}-H_{n})}{n(2)^n \binom{2n}{n}}$
Apr 7, 2022
4
Finding: $\int_0^\infty \frac{|\sin (ax)|^c - |\sin(bx)|^c}{x} \, dx$
Jun 15, 2022
4
Evaluate $\sum _{n=0}^{\infty } \frac{16^n}{(2n+1)^3 \binom{2 n}{n}^2}$
Jun 17, 2022