What is the integral from ln(pi) to 2 of e^xsin(e^x) ?

The integral from ln(pi) to 2 of e^xsin(e^x) is -cos(e^2)-1

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integral from ln(pi) to 2 of e^xsin(e^x)

\int_{l n (π)}^{2} e^{x} sin (e^{x}) d x

- cos (e^{2}) - 1

Decimal Notation

- 1.44835 \dots

Solution steps

\int_{l n (π)}^{2} e^{x} sin (e^{x}) d x

Apply u-substitution

: \int_{π}^{e^{2}} sin (u) d u

= \int_{π}^{e^{2}} sin (u) d u

Use the common integral:

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

= [- cos (u)]_{π}^{e^{2}}

Compute the boundaries:

- cos (e^{2}) - 1

= - cos (e^{2}) - 1

\int_{1}^{1.6} \frac{2 x}{x ^{2} - 4} d x

\int_{0}^{1} - x^{2} + x d x

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

\int_{1}^{5} 3 x + 1 d x

\int_{0}^{\frac{15}{16}} 1 + 16 x d x

What is the integral from ln(pi) to 2 of e^xsin(e^x) ?
The integral from ln(pi) to 2 of e^xsin(e^x) is -cos(e^2)-1