What is the integral from 2 to 3 of e^xcos(e^x) ?

The integral from 2 to 3 of e^xcos(e^x) is sin(e^3)-sin(e^2)

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integral from 2 to 3 of e^xcos(e^x)

\int_{2}^{3} e^{x} cos (e^{x}) d x

sin (e^{3}) - sin (e^{2})

Decimal

0.05061 \dots

Solution steps

\int_{2}^{3} e^{x} cos (e^{x}) d x

Apply u-substitution

: \int_{e^{2}}^{e^{3}} cos (u) d u

= \int_{e^{2}}^{e^{3}} cos (u) d u

Use the common integral:

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

= [sin (u)]_{e^{2}}^{e^{3}}

Compute the boundaries:

sin (e^{3}) - sin (e^{2})

= sin (e^{3}) - sin (e^{2})

\int_{a}^{b} 2 x d x

\int_{0}^{1} x^{2} sin (x) d x

\int_{0}^{\frac{π}{6}} (1 - cos (3 x)) sin (3 x) d x

\int_{1}^{9} \frac{x - 2 x ^{2}}{x} d x

\int_{\frac{π}{6}}^{\frac{π}{2}} sin (x) d x

What is the integral from 2 to 3 of e^xcos(e^x) ?
The integral from 2 to 3 of e^xcos(e^x) is sin(e^3)-sin(e^2)