What is the integral from 0 to ln(5x) of sin(4e^t) ?

The integral from 0 to ln(5x) of sin(4e^t) is \Si(20x)-1.75820…

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integral from 0 to ln(5x) of sin(4e^t)

\int_{0}^{l n (5 x)} sin (4 e^{t}) d t

Si (20 x) - 1.75820 \dots

Solution steps

\int_{0}^{l n (5 x)} sin (4 e^{t}) d t

Apply u-substitution

: \int_{4}^{20 x} \frac{sin ( u )}{u} d u

= \int_{4}^{20 x} \frac{sin ( u )}{u} d u

Use the nonelementary integral:

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

= [Si (u)]_{4}^{20 x}

Compute the boundaries:

Si (20 x) - 1.75820 \dots

= Si (20 x) - 1.75820 \dots

\int_{10}^{\infty} \frac{1}{x ^{2}} d x

\int_{0}^{0.5} b - 2 b x d x

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

\int_{0}^{l n (2)} e^{4 x} d x

\int_{0}^{2} 13 x^{2} d x

What is the integral from 0 to ln(5x) of sin(4e^t) ?
The integral from 0 to ln(5x) of sin(4e^t) is \Si(20x)-1.75820…