What is the integral from x to 5 of cos(e^t) ?

The integral from x to 5 of cos(e^t) is \Ci(e^5)-\Ci(e^x)

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integral from x to 5 of cos(e^t)

\int_{x}^{5} cos (e^{t}) d t

Ci (e^{5}) - Ci (e^{x})

Solution steps

\int_{x}^{5} cos (e^{t}) d t

Apply u-substitution

= \int_{e^{x}}^{e^{5}} \frac{cos ( u )}{u} d u

Use the nonelementary integral:

\int \frac{cos ( x )}{x} d x = Ci (x)

= [Ci (u)]_{e^{x}}^{e^{5}}

Compute the boundaries:

Ci (e^{5}) - Ci (e^{x})

= Ci (e^{5}) - Ci (e^{x})

\int_{1}^{3} \frac{1}{x - 1} d x

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

\int_{0}^{1} u d u

\int_{0}^{3} \frac{1}{1 + 1 + x} d x

\int_{- 1}^{2} (x) d x

What is the integral from x to 5 of cos(e^t) ?
The integral from x to 5 of cos(e^t) is \Ci(e^5)-\Ci(e^x)