Can this be proved using definite integrals
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
26501
Proof using complex numbers
45205
Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
51488
Evaluating $\int^\pi_{-\pi} \cos^3(x) \cos(ax)~dx$
67655
Simpler way to compute a definite integral without resorting to partial fractions?
87242
Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
128189
Proving Integral Inequality
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
75273
Help needed with definite integral for $\lim_{n\rightarrow \infty}\sum_{k=1}^{n} \frac{1}{n+k}$
115375
Indefinite integral of $e^{x^n}$
123695
Infinite series: Integral test( Proof )
82625
How do I prove this using question using Cauchy-Schwarz inequality?
67830
Evalute the definite integral: $\int_{0}^{3} (x^2+1) d[x]$
40272
Can we find a closed form for this integral?
136305
Is it possible? improper integral no answer?
110690
Real Analysis question on FTC, Integral