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Integral of (x-1)^1/2
Identical expressions
e^3sinx*cox
e cubed sinus of x multiply by cox
e3sinx*cox
e³sinx*cox
e to the power of 3sinx*cox
e^3sinxcox
e3sinxcox
e^3sinx*coxdx

Solving integrals/ e^3sinx*cox

Integral of e^3sinx*cox dx

The solution

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  1                    
  /                    
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 |   3                 
 |  e *sin(x)*cos(x) dx
 |                     
/                      
0

$$\int\limits_{0}^{1} e^{3} \sin{\left(x \right)} \cos{\left(x \right)}\, dx$$

Integral(E^3*sin(x)*cos(x), (x, 0, 1))

Detail solution

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

$\int e^{3} \sin{\left(x \right)} \cos{\left(x \right)}\, dx = e^{3} \int \sin{\left(x \right)} \cos{\left(x \right)}\, dx$
1. 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 $- du$ :
    
    $\int u\, du$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- u\right)\, du = - \int u\, du$
      
      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: $- \frac{u^{2}}{2}$
    Now substitute $u$ back in:
    
    $- \frac{\cos^{2}{\left(x \right)}}{2}$
  Method #2
  1. Let $u = \sin{\left(x \right)}$ .
    
    Then let $du = \cos{\left(x \right)} dx$ and substitute $du$ :
    
    $\int u\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    Now substitute $u$ back in:
    
    $\frac{\sin^{2}{\left(x \right)}}{2}$
So, the result is: $- \frac{e^{3} \cos^{2}{\left(x \right)}}{2}$
Add the constant of integration:

$- \frac{e^{3} \cos^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{e^{3} \cos^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                              2     3
 |  3                        cos (x)*e 
 | e *sin(x)*cos(x) dx = C - ----------
 |                               2     
/

$$-{{e^3\,\cos ^2x}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   2     3
sin (1)*e 
----------
    2

$$e^3\,\left({{1}\over{2}}-{{\cos ^21}\over{2}}\right)$$

   2     3
sin (1)*e 
----------
    2

$$\frac{e^{3} \sin^{2}{\left(1 \right)}}{2}$$

Упростить

Numerical answer [src]

7.11101739353076

7.11101739353076

The graph

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

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How to use it?

Identical expressions

Integral of e^3sinx*cox dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2