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Integral of d{x}:
Integral of x/e^x
Integral of xe^(x^2)
Integral of x²dx
Integral of ex
Identical expressions
(four cosx- two ^x*e^3x+ five /4+x^ two)
(4 co sinus of e of x minus 2 to the power of x multiply by e cubed x plus 5 divide by 4 plus x squared )
(four co sinus of e of x minus two to the power of x multiply by e cubed x plus five divide by 4 plus x to the power of two)
(4cosx-2x*e3x+5/4+x2)
4cosx-2x*e3x+5/4+x2
(4cosx-2^x*e³x+5/4+x²)
(4cosx-2 to the power of x*e to the power of 3x+5/4+x to the power of 2)
(4cosx-2^xe^3x+5/4+x^2)
(4cosx-2xe3x+5/4+x2)
4cosx-2xe3x+5/4+x2
4cosx-2^xe^3x+5/4+x^2
(4cosx-2^x*e^3x+5 divide by 4+x^2)
(4cosx-2^x*e^3x+5/4+x^2)dx
Similar expressions
(4cosx-2^x*e^3x+5/4-x^2)
(4cosx+2^x*e^3x+5/4+x^2)
(4cosx-2^x*e^3x-5/4+x^2)
What you mean?
4*cos(x) - 2^x*e^3*x + 5/4 + x^2
4*cos(x) - 2^((x*e)^(3*x)) + 5/4 + x^2
4*cos(x) - 2^x*e^(3*x + 5)/4 + x^2
4*cos(x) - 2^x*e^(3*x + 5)/4 + x^2

Solving integrals/ (4cosx-2^x*e^3x+5/4+x^2)

You entered:

(4cosx-2^x*e^3x+5/4+x^2)

What you mean?

4*cos(x) - 2^x*e^3*x + 5/4 + x^2

4*cos(x) - 2^((x*e)^(3*x)) + 5/4 + x^2

4*cos(x) - 2^x*e^(3*x + 5)/4 + x^2

4*cos(x) - 2^x*e^(3*x + 5)/4 + x^2

Integral of (4cosx-2^x*e^3x+5/4+x^2) dx

The solution

You have entered [src]

  1                                 
  /                                 
 |                                  
 |  /            x  3     5    2\   
 |  |4*cos(x) - 2 *e *x + - + x | dx
 |  \                     4     /   
 |                                  
/                                   
0

$$\int\limits_{0}^{1} \left(- 2^{x} x e^{3} + x^{2} + 4 \cos{\left(x \right)} + \frac{5}{4}\right)\, dx$$

Integral(4*cos(x) - 2^x*E^3*x + 5/4 + x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2^{x} x e^{3}\right)\, dx = - \int 2^{x} x e^{3}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2^{x} x e^{3}\, dx = e^{3} \int 2^{x} x\, dx$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $\frac{2^{x} \left(x \log{\left(2 \right)} - 1\right)}{\log{\left(2 \right)}^{2}}$
    So, the result is: $\frac{2^{x} \left(x \log{\left(2 \right)} - 1\right) e^{3}}{\log{\left(2 \right)}^{2}}$
  So, the result is: $- \frac{2^{x} \left(x \log{\left(2 \right)} - 1\right) e^{3}}{\log{\left(2 \right)}^{2}}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 \cos{\left(x \right)}\, dx = 4 \int \cos{\left(x \right)}\, dx$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $4 \sin{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \frac{5}{4}\, dx = \frac{5 x}{4}$
The result is: $- \frac{2^{x} \left(x \log{\left(2 \right)} - 1\right) e^{3}}{\log{\left(2 \right)}^{2}} + \frac{x^{3}}{3} + \frac{5 x}{4} + 4 \sin{\left(x \right)}$
Now simplify:

$- \frac{2^{x} x e^{3}}{\log{\left(2 \right)}} + \frac{2^{x} e^{3}}{\log{\left(2 \right)}^{2}} + \frac{x^{3}}{3} + \frac{5 x}{4} + 4 \sin{\left(x \right)}$
Add the constant of integration:

$- \frac{2^{x} x e^{3}}{\log{\left(2 \right)}} + \frac{2^{x} e^{3}}{\log{\left(2 \right)}^{2}} + \frac{x^{3}}{3} + \frac{5 x}{4} + 4 \sin{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- \frac{2^{x} x e^{3}}{\log{\left(2 \right)}} + \frac{2^{x} e^{3}}{\log{\left(2 \right)}^{2}} + \frac{x^{3}}{3} + \frac{5 x}{4} + 4 \sin{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                                  
 |                                                    3          x                  3
 | /            x  3     5    2\                     x    5*x   2 *(-1 + x*log(2))*e 
 | |4*cos(x) - 2 *e *x + - + x | dx = C + 4*sin(x) + -- + --- - ---------------------
 | \                     4     /                     3     4              2          
 |                                                                     log (2)       
/

$$4\,\sin x-{{\left(\log 2\,x-1\right)\,e^{\log 2\,x+3}}\over{\left( \log 2\right)^2}}+{{x^3}\over{3}}+{{5\,x}\over{4}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                    3                      3
19                 e      2*(-1 + log(2))*e 
-- + 4*sin(1) - ------- - ------------------
12                 2              2         
                log (2)        log (2)

$${{\left(48\,\sin 1+19\right)\,\left(\log 2\right)^2-24\,e^3\,\log 2 +12\,e^3}\over{12\,\left(\log 2\right)^2}}$$

                    3                      3
19                 e      2*(-1 + log(2))*e 
-- + 4*sin(1) - ------- - ------------------
12                 2              2         
                log (2)        log (2)

$$- \frac{e^{3}}{\log{\left(2 \right)}^{2}} + \frac{19}{12} + 4 \sin{\left(1 \right)} - \frac{2 \left(-1 + \log{\left(2 \right)}\right) e^{3}}{\log{\left(2 \right)}^{2}}$$

Simplify

Numerical answer [src]

-11.1999782340195

-11.1999782340195

The graph

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

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You entered:

What you mean?

Integral of (4cosx-2^x*e^3x+5/4+x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution