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

The integral from 0 to ln(pi) of e^xcos(e^x) is -sin(1)

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(pi) of e^xcos(e^x)

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

- sin (1)

Solution steps

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

Apply u-substitution

: \int_{1}^{π} cos (u) d u

= \int_{1}^{π} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= [sin (u)]_{1}^{π}

Compute the boundaries:

- sin (1)

= - sin (1)

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

\int_{2}^{8} ∣ sin (x) ∣ d x

\int_{2}^{4} 4^{2 x} d x

\int_{0}^{z} \frac{z}{x ^{2} + z ^{2}} d x

\int_{2}^{3} 4^{5 x} d x

What is the integral from 0 to ln(pi) of e^xcos(e^x) ?
The integral from 0 to ln(pi) of e^xcos(e^x) is -sin(1)