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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int_{e^{y}}^{e^{x}} \frac{cos ( u )}{u} d u

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

Use the nonelementary integral:

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

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

Compute the boundaries:

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

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

\frac{d}{d t} (t + \frac{1}{t})

\int (2 a^{2} x^{2} - b^{3})^{2} d x

\int 6 e^{2 t} d t

\int \frac{1}{2} sec^{2} (x) d x

\frac{\partial}{\partial x} (x^{2} y^{3})

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