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sec(x)
Solving integrals/ sec(x)

Integral of sec(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
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 |  sec(x) dx
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0
$$\int\limits_{0}^{1} \sec{\left(x \right)}\, dx$$ 
Integral(sec(x), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. Let .

    Then let and substitute :

    1. The integral of is .

    Now substitute back in:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                    
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 | sec(x) dx = C + log(sec(x) + tan(x))
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$$\int \sec{\left(x \right)}\, dx = C + \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(1 + sin(1))   log(1 - sin(1))
--------------- - ---------------
       2                 2
$$\frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{2} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{2}$$ 
=
= 
log(1 + sin(1))   log(1 - sin(1))
--------------- - ---------------
       2                 2
$$\frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{2} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{2}$$ 
log(1 + sin(1))/2 - log(1 - sin(1))/2
Numerical answer [src] 
1.22619117088352
1.22619117088352
The graph
Integral of sec(x) dx

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

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