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Identical expressions
(twelve ^(sinx))*cosx
(12 to the power of ( sinus of x)) multiply by co sinus of e of x
(twelve to the power of ( sinus of x)) multiply by co sinus of e of x
(12(sinx))*cosx
12sinx*cosx
(12^(sinx))cosx
(12(sinx))cosx
12sinxcosx
12^sinxcosx
(12^(sinx))*cosxdx

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

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

Let $u = \sin{\left(x \right)}$ .

Then let $du = \cos{\left(x \right)} dx$ and substitute $du$ :

$\int 12^{u}\, du$
1. The integral of an exponential function is itself divided by the natural logarithm of the base.
  
  $\int 12^{u}\, du = \frac{12^{u}}{\log{\left(12 \right)}}$
Now substitute $u$ back in:

$\frac{12^{\sin{\left(x \right)}}}{\log{\left(12 \right)}}$
Add the constant of integration:

$\frac{12^{\sin{\left(x \right)}}}{\log{\left(12 \right)}}+ \mathrm{constant}$

The answer is:

$\frac{12^{\sin{\left(x \right)}}}{\log{\left(12 \right)}}+ \mathrm{constant}$

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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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution