If $ f(x) = x^3+\frac{3x}{4}-\frac{3x^2}{2}+\frac{7}{8}.$ Then $ \int^{\frac{3}{4}}_{\frac{1}{4}}f(f(x))dx$
112778
Let $f(x) = x^3-\frac{3}{2}x^2+x+\frac{1}{4}.$ Then the value of $ \int^{3/4}_{1/4}f(f(x))\mathrm dx$
143236
$ S_{n}=\frac{x}{x+1}+\frac{x^2}{(x+1)(x^2+1)}+...........+\frac{x^{2^{n}}}{(x+1)(x^2+1)...(x^{2^{n}}+1)}$
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
4971
$\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$
86247
$ \int\frac{g(x)}{f(x)} \, dx $ where $f(x) = \frac{1}{2}(e^x+e^{-x})$ and $g(x) = \frac{1}{2}(e^x - e^{-x})$?
49944
Integral $\int_1^3 \frac{\log x}{x^2+3}dx$
117046
Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$
42699
Solve for $f(x)$ if $f(f(x))=6x-f(x)$
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
107133
Let f(x) be a polynomial satisfying $\lim_{x \to\infty} \frac{x^4f(x)}{x^8+1}=3,$ $f(2)=5 $ and $f(3)=10$, $f(-1)=2$ and $f(-6)=37$
133990
How prove this $\int_{a}^{b}f(x)dx=\frac{1}{2}(b-a)[f(a)+f(b)]-\frac{1}{12}(b-a)^3f''(\xi)$
53519
Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
61466
what is $\int_{|z|=3}\frac{1}{(z-2)^n(z-4)^m}dz$ for $m,n\in\mathbb{N}$?
13287
Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$
106013
Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable
99584
Evaluation of $\int \frac{\sqrt{\sin ^4x+\cos ^4x}}{\sin ^3x \cos x }dx$