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e^2cosx*sinx
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e^2cosx*sinxdx

Integral of e^2cosx*sinx dx

The solution

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  0                    
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 |   2                 
 |  E *cos(x)*sin(x) dx
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0

$$\int\limits_{0}^{0} e^{2} \cos{\left(x \right)} \sin{\left(x \right)}\, dx$$

Integral((E^2*cos(x))*sin(x), (x, 0, 0))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = \cos{\left(x \right)}$ .
  
  Then let $du = - \sin{\left(x \right)} dx$ and substitute $- du e^{2}$ :
  
  $\int \left(- u e^{2}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u\, du = - e^{2} \int u\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    So, the result is: $- \frac{u^{2} e^{2}}{2}$
  Now substitute $u$ back in:
  
  $- \frac{e^{2} \cos^{2}{\left(x \right)}}{2}$
Method #2
1. Let $u = \sin{\left(x \right)}$ .
  
  Then let $du = \cos{\left(x \right)} dx$ and substitute $du e^{2}$ :
  
  $\int u e^{2}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u\, du = e^{2} \int u\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    So, the result is: $\frac{u^{2} e^{2}}{2}$
  Now substitute $u$ back in:
  
  $\frac{e^{2} \sin^{2}{\left(x \right)}}{2}$
Add the constant of integration:

$- \frac{e^{2} \cos^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{e^{2} \cos^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                              2     2
 |  2                        cos (x)*e 
 | E *cos(x)*sin(x) dx = C - ----------
 |                               2     
/

$$\int e^{2} \cos{\left(x \right)} \sin{\left(x \right)}\, dx = C - \frac{e^{2} \cos^{2}{\left(x \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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How to use it?

Identical expressions

Integral of e^2cosx*sinx dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2