What is the integral from x to y of cos(e^t) ?

The integral from x to y of cos(e^t) is \Ci(e^y)-\Ci(e^x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from x to y of cos(e^t)

\int_{x}^{y} cos (e^{t}) d t

Ci (e^{y}) - Ci (e^{x})

Solution steps

\int_{x}^{y} cos (e^{t}) d t

Apply u-substitution

: \int_{e^{x}}^{e^{y}} \frac{cos ( u )}{u} d u

= \int_{e^{x}}^{e^{y}} \frac{cos ( u )}{u} d u

Use the nonelementary integral:

\int \frac{cos ( x )}{x} d x = Ci (x)

= [Ci (u)]_{e^{x}}^{e^{y}}

Compute the boundaries:

Ci (e^{y}) - Ci (e^{x})

= Ci (e^{y}) - Ci (e^{x})

\int_{0}^{2 π} 3 sin (\frac{x}{2}) d x

\int_{1}^{4} \frac{x ^{2}}{x ^{2} + 4} d x

\int_{2}^{6} x - 1 d x

\int_{0}^{1} x e^{x} ln (2) d x

\int_{1}^{2} \frac{e ^{x}}{e ^{x} + e} d x

What is the integral from x to y of cos(e^t) ?
The integral from x to y of cos(e^t) is \Ci(e^y)-\Ci(e^x)