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

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

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integral from 0 to 1 of e^xcos(e^x)

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

sin (e) - sin (1)

Decimal Notation

- 0.43068 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{e} cos (u) d u

= \int_{1}^{e} cos (u) d u

Use the common integral:

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

= [sin (u)]_{1}^{e}

Compute the boundaries:

sin (e) - sin (1)

= sin (e) - sin (1)

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

\int_{99}^{100} (x^{2} + 1) d x

\int_{x}^{2} \frac{1}{2} d y

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