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…

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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

= \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

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\int_{- 3}^{3} 2 9 - x^{2} d x

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…