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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Si (x) - 0.9460830704

Solution steps

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

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

\int \frac{x}{5 - x ^{2}} d x

\int arcsin (u) d u

\int_{0}^{x} 1 d x

\frac{d}{d x} ((5 x + 1)^{2})

f (θ) = 3 sec (θ)

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