What is the integral from 0 to ln(2x) of sin(6e^t) ?

The integral from 0 to ln(2x) of sin(6e^t) is \Si(12x)-1.42468…

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integral from 0 to ln(2x) of sin(6e^t)

\int_{0}^{l n (2 x)} sin (6 e^{t}) d t

Si (12 x) - 1.42468 \dots

Solution steps

\int_{0}^{l n (2 x)} sin (6 e^{t}) d t

Apply u-substitution

: \int_{6}^{12 x} \frac{sin ( u )}{u} d u

= \int_{6}^{12 x} \frac{sin ( u )}{u} d u

Use the nonelementary integral:

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

= [Si (u)]_{6}^{12 x}

Compute the boundaries:

Si (12 x) - 1.42468 \dots

= Si (12 x) - 1.42468 \dots

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\int_{0}^{π} sin^{3} (t) d t

\int_{1}^{2} x \cdot e^{- x} d x

\int_{0}^{1} n x (1 - x^{2})^{n} d x

What is the integral from 0 to ln(2x) of sin(6e^t) ?
The integral from 0 to ln(2x) of sin(6e^t) is \Si(12x)-1.42468…