How to simplify expression $\int_a^b f(x)dx+\int_{f(a)}^{f(b)} f^{-1}(x)dx \ ?$
36093
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
67830
Evalute the definite integral: $\int_{0}^{3} (x^2+1) d[x]$
67565
If $\int^x_0 f (t) dt =x+ \int^1_x t f (t) dt$, find value of $f(1)$
63251
Evaluation of $\int^1_0\frac{x^b-x^a}{\ln x} d x=\ln{{\frac{1+b}{1+a}}}$
53518
Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
150809
Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$
86367
Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$
132383
Evaluate the integral $\int_{-1}^1\frac{dx}{(e^x+1)(x^2+1)}$.
61162
Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $
58832
How prove this $\int_{a}^{b}[f''(x)]^2dx\ge\dfrac{4}{b-a}$
127558
If $f(x)=x-\int^{\frac{\pi}{2}}_0f(x)\sin(x)dx$ find the explicit function for $f(x)$ in its simplest form
148826
Integral of $ 1 \, / \, (1 + a \, \cos(x) )$
85085
Simplifying the derivative of $|x|$
17532
Why does Simplify[b-a] give -a+b and not b-a?
133851
How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$