Jun 14, 2017 · Closed 8 years ago. I was having trouble with the following integral: $\int_ {0}^\infty \frac {\sin (x)} {x}dx$. My question is, how does one go about evaluating this, since its existence seems …

The indefinite integral, you mean. Of course, $\mathrm {Si} (x)$ is simply defined to be a definite integral of $ (\sin x)/x$, so of course you're going to get this plus a constant.

May 6, 2020 · Definite integral of $\sin (x)/x$ Ask Question Asked 5 years, 8 months ago Modified 5 years, 8 months ago

May 6, 2012 · how to calculate the integral of $\sin^2 (x)/x^2$ [duplicate] Ask Question Asked 13 years, 8 months ago Modified 2 years, 2 months ago

$\int \sin^n {x} \ dx = \sin^ {n - 1} {x} \cdot \sin {x} \ dx$ $\int \sin^n {x} \ dx = \underbrace {\sin^ {n - 1} {x}}_ {u} \cdot \underbrace {-\cos {x}}_ {v} - \int ...

Improper integral $\sin (x)/x $ converges absolutely, conditionally or diverges? Ask Question Asked 12 years, 7 months ago Modified 1 year, 4 months ago

Sep 26, 2018 · Therefore integral $\int\limits_0^ {1}x^ {\epsilon}\ln (\sin (x)) dx$ exists and of course $\int\limits_0^ {\frac {\pi} {2}}x^ {\epsilon}\ln (\sin (x)) dx$. So by comparison test $\int\limits_0^ {\frac …

Apr 4, 2019 · Integral of the absolute value of sin (x)/x Ask Question Asked 6 years, 9 months ago Modified 1 year, 1 month ago

Apr 12, 2016 · An aside, unrelated to the question: for one of my favorite integral tricks, look up Feynman's trick-- or, more objectively, "differentiating parameters under an integral." One of the …

Nov 10, 2020 · While watching this video, he says that $$\lim_ {b\to\infty}\int_0^\infty \frac {\sin x} {x}e^ {-bx}dx\to 0$$ since the integrand tends to $0$. However I think that it must be an indeterminate form, …