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Solving integrals/ e^(sinx)*cosx

Integral of e^(sinx)*cosx dx

The solution

You have entered [src]

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

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

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

Detail solution

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

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

$\int e^{u}\, du$
1. The integral of the exponential function is itself.
  
  $\int e^{u}\, du = e^{u}$
Now substitute $u$ back in:

$e^{\sin{\left(x \right)}}$
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)
 | E      *cos(x) dx = C + e      
 |                                
/

$$\int e^{\sin{\left(x \right)}} \cos{\left(x \right)}\, dx = C + e^{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      sin(1)
-1 + e

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

      sin(1)
-1 + e

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

-1 + exp(sin(1))

Numerical answer [src]

1.31977682471585

1.31977682471585

The graph

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

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Identical expressions

Similar expressions

Integral of e^(sinx)*cosx dx

Limits of integration:

The graph:

Piecewise:

The solution