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Integral of √(x+4)
Identical expressions
e^-x^ four +5x^3dx
e to the power of minus x to the power of 4 plus 5x cubed dx
e to the power of minus x to the power of four plus 5x cubed dx
e-x4+5x3dx
e^-x⁴+5x³dx
e to the power of -x to the power of 4+5x to the power of 3dx
Similar expressions
e^+x^4+5x^3dx
e^-x^4-5x^3dx
What you mean?
e^((-x)^4) + 5*x^3*dx
e^(-x^4) + 5*x^3*dx
e^(-x^4) + 5*x^3*dx

You entered:

e^-x^4+5x^3dx

What you mean?

e^((-x)^4) + 5*x^3*dx

e^(-x^4) + 5*x^3*dx

e^(-x^4) + 5*x^3*dx

Integral of e^-x^4+5x^3dx dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  /   4         \   
 |  | -x       3  |   
 |  \e    + 5*x *1/ dx
 |                    
/                     
0

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

Integral(E^(-x^4) + 5*x^3*1, (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:
  
  $\int 5 x^{3} \cdot 1\, dx = 5 \int x^{3}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $\frac{5 x^{4}}{4}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{\Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, x^{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$
The result is: $\frac{5 x^{4}}{4} + \frac{\Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, x^{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$
Now simplify:

$\frac{5 x^{4}}{4} + \frac{\gamma\left(\frac{1}{4}, x^{4}\right)}{4}$
Add the constant of integration:

$\frac{5 x^{4}}{4} + \frac{\gamma\left(\frac{1}{4}, x^{4}\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{5 x^{4}}{4} + \frac{\gamma\left(\frac{1}{4}, x^{4}\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                              
 |                                                               
 | /   4         \             4                        /      4\
 | | -x       3  |          5*x    Gamma(1/4)*lowergamma\1/4, x /
 | \e    + 5*x *1/ dx = C + ---- + ------------------------------
 |                           4             16*Gamma(5/4)         
/

$$\int \left(5 x^{3} \cdot 1 + e^{- x^{4}}\right)\, dx = C + \frac{5 x^{4}}{4} + \frac{\Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, x^{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5   Gamma(1/4)*lowergamma(1/4, 1)
- + -----------------------------
4           16*Gamma(5/4)

$$\frac{\Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, 1\right)}{16 \Gamma\left(\frac{5}{4}\right)} + \frac{5}{4}$$

5   Gamma(1/4)*lowergamma(1/4, 1)
- + -----------------------------
4           16*Gamma(5/4)

$$\frac{\Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, 1\right)}{16 \Gamma\left(\frac{5}{4}\right)} + \frac{5}{4}$$

Упростить

Numerical answer [src]

2.0948385947571

2.0948385947571

The graph

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

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What you mean?

Integral of e^-x^4+5x^3dx dx

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The graph:

Piecewise:

The solution