What is the integral of cos(e^x) ?

The integral of cos(e^x) is \Ci(e^x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(e^x)

\int cos (e^{x}) d x

Ci (e^{x}) + C

Solution steps

\int cos (e^{x}) d x

Apply u-substitution

: \int \frac{cos ( u )}{u} d u

= \int \frac{cos ( u )}{u} d u

Use the nonelementary integral:

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

= Ci (u)

Substitute back

u = e^{x}

= Ci (e^{x})

Add a constant to the solution

= Ci (e^{x}) + C

\int (1 - cos (x))^{\frac{1}{2}} d x

\int (4 x^{3} - 2 sec^{2} (x)) d x

\frac{\partial}{\partial x} (9 x y - x^{3} - y^{3} - 6)

\int \frac{sin ( 8 x )}{1 + cos ^{2} ( 8 x )} d x

\frac{d}{d x} (\frac{x + 1}{x})