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Integral of 4^cosx*sinxdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |   cos(x)          
 |  4      *sin(x) dx
 |                   
/                    
0                    
$$\int\limits_{0}^{1} 4^{\cos{\left(x \right)}} \sin{\left(x \right)}\, dx$$
Integral(4^cos(x)*sin(x), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

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

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                               
 |                          cos(x)
 |  cos(x)                 4      
 | 4      *sin(x) dx = C - -------
 |                          log(4)
/                                 
$$\int 4^{\cos{\left(x \right)}} \sin{\left(x \right)}\, dx = - \frac{4^{\cos{\left(x \right)}}}{\log{\left(4 \right)}} + C$$
The graph
The answer [src]
          cos(1) 
  2      4       
------ - --------
log(2)   2*log(2)
$$- \frac{4^{\cos{\left(1 \right)}}}{2 \log{\left(2 \right)}} + \frac{2}{\log{\left(2 \right)}}$$
=
=
          cos(1) 
  2      4       
------ - --------
log(2)   2*log(2)
$$- \frac{4^{\cos{\left(1 \right)}}}{2 \log{\left(2 \right)}} + \frac{2}{\log{\left(2 \right)}}$$
2/log(2) - 4^cos(1)/(2*log(2))
Numerical answer [src]
1.35979617708281
1.35979617708281

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