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

The integral from 0 to ln(x) of sin(e^t) is \Si(x)-0.9460830704

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

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

Si (x) - 0.9460830704

Solution steps

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

Apply u-substitution

: \int_{1}^{x} \frac{sin ( u )}{u} d u

= \int_{1}^{x} \frac{sin ( u )}{u} d u

Use the nonelementary integral:

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

= [Si (u)]_{1}^{x}

Compute the boundaries:

Si (x) - 0.9460830704

= Si (x) - 0.9460830704

\frac{d}{d x} ((3 x^{2} + 4 x + 8) x - 1)

n = 3 \sum \infty \frac{8}{n ^{2} - 1}

4 x^{3} + 6 x^{2}

\frac{\partial}{\partial x} (6 x + 3 y - 7)

\frac{d}{d y} (2 e^{y})

What is the integral from 0 to ln(x) of sin(e^t) ?
The integral from 0 to ln(x) of sin(e^t) is \Si(x)-0.9460830704