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Solving integrals/ cos(e^x)

Integral of cos(e^x) dx

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$$\int\limits_{0}^{1} \cos{\left(e^{x} \right)}\, dx$$

Integral(cos(E^x), (x, 0, 1))

Detail solution

Let $u = e^{x}$ .

Then let $du = e^{x} dx$ and substitute $du$ :

$\int \frac{\cos{\left(u \right)}}{u}\, du$
Now substitute $u$ back in:

$\operatorname{Ci}{\left(e^{x} \right)}$
Now simplify:

$\operatorname{Ci}{\left(e^{x} \right)}$
Add the constant of integration:

$\operatorname{Ci}{\left(e^{x} \right)}+ \mathrm{constant}$

The answer is:

$\operatorname{Ci}{\left(e^{x} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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$$\int \cos{\left(e^{x} \right)}\, dx = C + \operatorname{Ci}{\left(e^{x} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-Ci(1) + Ci(E)

$$- \operatorname{Ci}{\left(1 \right)} + \operatorname{Ci}{\left(e \right)}$$

-Ci(1) + Ci(E)

$$- \operatorname{Ci}{\left(1 \right)} + \operatorname{Ci}{\left(e \right)}$$

-Ci(1) + Ci(E)

Numerical answer [src]

-0.123445921560588

-0.123445921560588

The graph

Use the examples entering the upper and lower limits of integration.