Integral of cosxe^sinx dx

The solution

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  1                  
  /                  
 |                   
 |          sin(x)   
 |  cos(x)*e       dx
 |                   
/                    
0

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

Integral(cos(x)*E^sin(x), (x, 0, 1))

Detail solution

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

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

$\int 1\, du$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, du = u$
Now substitute $u$ back in:

$e^{\sin{\left(x \right)}}$
Now simplify:

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

$e^{\sin{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$e^{\sin{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |         sin(x)           sin(x)
 | cos(x)*e       dx = C + e      
 |                                
/

$$e^{\sin x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      sin(1)
-1 + e

$$e^{\sin 1}-1$$

      sin(1)
-1 + e

$$-1 + e^{\sin{\left(1 \right)}}$$

Simplify

Numerical answer [src]

1.31977682471585

1.31977682471585

The graph

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

Other calculators

How to use it?

Identical expressions

Integral of cosxe^sinx dx

Limits of integration:

The graph:

Piecewise:

The solution