Integral of cos^xdx dx

The solution

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  1           
  /           
 |            
 |     x      
 |  cos (1) dx
 |            
/             
0

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

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

Detail solution

The integral of an exponential function is itself divided by the natural logarithm of the base.

$\int \cos^{x}{\left(1 \right)}\, dx = \frac{\cos^{x}{\left(1 \right)}}{\log{\left(\cos{\left(1 \right)} \right)}}$
Add the constant of integration:

$\frac{\cos^{x}{\left(1 \right)}}{\log{\left(\cos{\left(1 \right)} \right)}}+ \mathrm{constant}$

The answer is:

$\frac{\cos^{x}{\left(1 \right)}}{\log{\left(\cos{\left(1 \right)} \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                       x     
 |    x               cos (1)  
 | cos (1) dx = C + -----------
 |                  log(cos(1))
/

$$\int \cos^{x}{\left(1 \right)}\, dx = C + \frac{\cos^{x}{\left(1 \right)}}{\log{\left(\cos{\left(1 \right)} \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

       1           cos(1)  
- ----------- + -----------
  log(cos(1))   log(cos(1))

$$\frac{\cos{\left(1 \right)}}{\log{\left(\cos{\left(1 \right)} \right)}} - \frac{1}{\log{\left(\cos{\left(1 \right)} \right)}}$$

       1           cos(1)  
- ----------- + -----------
  log(cos(1))   log(cos(1))

$$\frac{\cos{\left(1 \right)}}{\log{\left(\cos{\left(1 \right)} \right)}} - \frac{1}{\log{\left(\cos{\left(1 \right)} \right)}}$$

-1/log(cos(1)) + cos(1)/log(cos(1))

Numerical answer [src]

0.746715283122276

0.746715283122276

The graph

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

Other calculators

How to use it?

Identical expressions

Integral of cos^xdx dx

Limits of integration:

The graph:

Piecewise:

The solution