Let $x > 0$. Prove that the value of $\int^{x}_{0} \frac{1}{1+t^2}dt + \int^{\frac{1}{x}}_{0} \frac{1}{1+t^2}dt$ does not depend on $x$.
110327
How to do this question that talks about dependency of x
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
109099
Prove that $\lim_{h \to 0}\frac{1}{h}\int_0^h{\cos{\frac{1}{t}}dt} = 0$
147108
Prove that $\int_0^\infty \frac{x\,\log x}{(1+x^2)^2} = 0$
139742
Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
4656
Prove that there is a $\delta$ such that $\int_{0}^{1} (f(x))^2dx\leq \delta$$\int_{0}^{1} (f'(x))^2dx$ for all $f$ with these conditions
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
88259
prove that $\frac{1}{x}$ is not uniformly continuous on $(0,1)$
104853
Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$
7192
Integral inequality with a strange condition
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
103495
Let $f$ be continuous. Then $\int_{0}^{x}\left[\int_{0}^{t}f\left(u\right)du\right]dt=\int_{0}^{x}f\left(u\right)\left(x-u\right)du$
4278
Is $\frac{\vert x+y\vert}{1+\vert x+y\vert}\leq\frac{\vert x\vert}{1+\vert x\vert}+\frac{\vert y\vert}{1+\vert y\vert}$ true?
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
124026
Prove $\int^\infty_0\frac x{e^x-1}dx=\frac{\pi^2}{6}$
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist