Mister Exam

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Identical expressions
e^sinx×cosx
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esinx×cosx
e^sinx×cosxdx

Solving integrals/ e^sinx×cosx

Integral of e^sinx×cosx dx

The solution

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 pi                  
  /                  
 |                   
 |   sin(x)          
 |  e      *cos(x) dx
 |                   
/                    
pi                   
--                   
2

$$\int\limits_{\frac{\pi}{2}}^{\pi} e^{\sin{\left(x \right)}} \cos{\left(x \right)}\, dx$$

Integral(E^sin(x)*cos(x), (x, pi/2, pi))

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)
 | 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]

1 - e

$$1 - e$$

1 - e

$$1 - e$$

Упростить

Numerical answer [src]

-1.71828182845905

-1.71828182845905

The graph

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

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Identical expressions

Integral of e^sinx×cosx dx

Limits of integration:

The graph:

Piecewise:

The solution