What is the integral from 0 to ln(4x) of sin(6e^t) ?

The integral from 0 to ln(4x) of sin(6e^t) is \Si(24x)-1.42468…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to ln(4x) of sin(6e^t)

\int_{0}^{l n (4 x)} sin (6 e^{t}) d t

Si (24 x) - 1.42468 \dots

Solution steps

\int_{0}^{l n (4 x)} sin (6 e^{t}) d t

Apply u-substitution

= \int_{6}^{24 x} \frac{sin ( u )}{u} d u

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= [Si (u)]_{6}^{24 x}

Compute the boundaries:

Si (24 x) - 1.42468 \dots

= Si (24 x) - 1.42468 \dots

What is the integral from 0 to ln(4x) of sin(6e^t) ?
The integral from 0 to ln(4x) of sin(6e^t) is \Si(24x)-1.42468…