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

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

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integral from 0 to pi of e^xcos(e^x)

\int_{0}^{π} e^{x} cos (e^{x}) d x

sin (e^{π}) - sin (1)

Decimal

- 1.75404 \dots

Solution steps

\int_{0}^{π} e^{x} cos (e^{x}) d x

Apply u-substitution

: \int_{1}^{e^{π}} cos (u) d u

= \int_{1}^{e^{π}} cos (u) d u

Use the common integral:

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

= [sin (u)]_{1}^{e^{π}}

Compute the boundaries:

sin (e^{π}) - sin (1)

= sin (e^{π}) - sin (1)

\int_{0}^{19 π} sin (x) d x

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

\int_{- 2}^{3} (x + 4) - (x^{2} - 2) d x

\int_{0}^{6} e^{x^{2}} d x

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