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  • Identical expressions

  • (twelve ^(sinx))*cosx
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  • (twelve to the power of ( sinus of x)) multiply by co sinus of e of x
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  • (12^(sinx))*cosxdx
Solving integrals/ (12^(sinx))*cosx

Integral of (12^(sinx))*cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                   
 --                   
 2                    
  /                   
 |                    
 |    sin(x)          
 |  12      *cos(x) dx
 |                    
/                     
0
$$\int\limits_{0}^{\frac{\pi}{2}} 12^{\sin{\left(x \right)}} \cos{\left(x \right)}\, dx$$ 
Integral(12^sin(x)*cos(x), (x, 0, pi/2))
Detail solution

  1. Let .

    Then let and substitute :

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

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                 
 |                            sin(x)
 |   sin(x)                 12      
 | 12      *cos(x) dx = C + --------
 |                          log(12) 
/
$$\int 12^{\sin{\left(x \right)}} \cos{\left(x \right)}\, dx = \frac{12^{\sin{\left(x \right)}}}{\log{\left(12 \right)}} + C$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   11  
-------
log(12)
$$\frac{11}{\log{\left(12 \right)}}$$ 
=
= 
   11  
-------
log(12)
$$\frac{11}{\log{\left(12 \right)}}$$ 
11/log(12)
Numerical answer [src] 
4.42672564820029
4.42672564820029

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

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