calculate $\int_{-a}^a \frac{f(x)}{1+e^x}dx$
62524
Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even
112621
Finding $\int_{0}^{\infty} \frac{e^{3x}-e^x}{x(e^{3x}+1)(e^x+1)} dx$
144942
Obtain the value of $\int_0^1f(x) \ dx$, where $f(x) = \begin{cases} \frac {1}{n}, & \frac{1}{n+1}<x\le\frac{1}{n}\\ 0, & x=0 \end{cases}$
8606
Calculate $\int^{n+1}_1 \frac{(\{x\})^{[x]}}{[x]}dx$ where $n\in\mathbb{N}$, $[x]$ is the integer part of $x$ and $\left\{ x\right\} =x-[x]$.
17454
Evaluate the integral $\int_0^n \frac{f(x)}{f(x) + f(n-x)}dx $
150809
Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$
27195
Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
6014
Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
133990
How prove this $\int_{a}^{b}f(x)dx=\frac{1}{2}(b-a)[f(a)+f(b)]-\frac{1}{12}(b-a)^3f''(\xi)$
86247
$ \int\frac{g(x)}{f(x)} \, dx $ where $f(x) = \frac{1}{2}(e^x+e^{-x})$ and $g(x) = \frac{1}{2}(e^x - e^{-x})$?
126054
calculate $\int_o^\pi \frac{x\sin x}{1+\cos^2x} \,dx$
53518
Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
44059
Evaluating $\int_{-1}^{1}\frac{\arctan{x}}{1+x}\ln{\left(\frac{1+x^2}{2}\right)}dx$
106587
Calculation of an integral with a Bessel function
100194
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
145590
Compute the integral $\int\frac{dx}{(x^2-x+1)\sqrt{x^2+x+1}}$
145403
Stuck in integration: $\int {\frac{dx}{( 1+\sqrt {x})\sqrt{(x-{x}^2)}}}$