Proof of integral identity using integration by parts
36093
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$
99001
General identity for a double summation theorem
10675
Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
34905
Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$
98344
Prove that $\int_0^1[f''(x)]^2dx\ge4.$
48881
Verification the integral identity $\int_0^\pi \ln(1+\alpha\cos(x))dx=\pi\ln\left(\frac{1+\sqrt{1-\alpha^2}}{2}\right)$.
59792
Can someone explain how integration by parts was done?
114411
Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$
65983
Combinatorial proof of binomial coefficient summation identity
77253
Proof of Lagrange Identity
75501
Proof using Cauchy Integral Theorem
102704
Prove an identity for the continuous integral solution of the conservation law
45725
Derivation of an identity with beta function.
144018
Integration by parts for f(x).g(x)
62192
Proof $L{\rm{[}}\frac{{x(t)}}{t}{\rm{] = }}\int_s^\infty {X(u)du} $
33617
Prove the inequality involving multiple integrals
133990
How prove this $\int_{a}^{b}f(x)dx=\frac{1}{2}(b-a)[f(a)+f(b)]-\frac{1}{12}(b-a)^3f''(\xi)$