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

The integral from 0 to 1 of e^xsin(e^x) is -cos(e)+cos(1)

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

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

- cos (e) + cos (1)

Decimal

1.45203 \dots

Solution steps

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

Apply u-substitution

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

Use the common integral:

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

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

Compute the boundaries:

- cos (e) + cos (1)

= - cos (e) + cos (1)

What is the integral from 0 to 1 of e^xsin(e^x) ?
The integral from 0 to 1 of e^xsin(e^x) is -cos(e)+cos(1)