Mister Exam

Other calculators

(x^4*(dx))/(sqrt(1+3x^3))

  • How to use it?

  • Integral of d{x}:
  • Integral of sin(5x) Integral of sin(5x)
  • Integral of x^3/(x+1) Integral of x^3/(x+1)
  • Integral of 2/(x^2-1) Integral of 2/(x^2-1)
  • Integral of (x+2)dx Integral of (x+2)dx

  • Identical expressions

  • (x^ four *(dx))/(sqrt(one + three x^3))
  • (x to the power of 4 multiply by (dx)) divide by ( square root of (1 plus 3x cubed ))
  • (x to the power of four multiply by (dx)) divide by ( square root of (one plus three x cubed ))
  • (x^4*(dx))/(√(1+3x^3))
  • (x4*(dx))/(sqrt(1+3x3))
  • x4*dx/sqrt1+3x3
  • (x⁴*(dx))/(sqrt(1+3x³))
  • (x to the power of 4*(dx))/(sqrt(1+3x to the power of 3))
  • (x^4(dx))/(sqrt(1+3x^3))
  • (x4(dx))/(sqrt(1+3x3))
  • x4dx/sqrt1+3x3
  • x^4dx/sqrt1+3x^3
  • (x^4*(dx)) divide by (sqrt(1+3x^3))

  • Similar expressions

  • (x^4*(dx))/(sqrt(1-3x^3))
Solving integrals/ (x^4*(dx))/(sqrt(1+3x^3))

Integral of (x^4*(dx))/(sqrt(1+3x^3)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                      
  /                      
 |                       
 |   4         1         
 |  x *1*------------- dx
 |          __________   
 |         /        3    
 |       \/  1 + 3*x     
 |                       
/                        
0
$$\int\limits_{0}^{1} x^{4} \cdot 1 \cdot \frac{1}{\sqrt{3 x^{3} + 1}}\, dx$$ 
Integral(x^4*1/sqrt(1 + 3*x^3), (x, 0, 1))
The answer (Indefinite) [src] 
                                               _                         
  /                             5             |_  /1/2, 5/3 |    3  pi*I\
 |                             x *Gamma(5/3)* |   |         | 3*x *e    |
 |  4         1                              2  1 \  8/3    |           /
 | x *1*------------- dx = C + ------------------------------------------
 |         __________                         3*Gamma(8/3)               
 |        /        3                                                     
 |      \/  1 + 3*x                                                      
 |                                                                       
/
$$\int {{{x^4}\over{\sqrt{3\,x^3+1}}}}{\;dx}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
             _                      
            |_  /1/2, 5/3 |    pi*I\
Gamma(5/3)* |   |         | 3*e    |
           2  1 \  8/3    |        /
------------------------------------
            3*Gamma(8/3)
$$\int_{0}^{1}{{{x^4}\over{\sqrt{3\,x^3+1}}}\;dx}$$ 
=
= 
             _                      
            |_  /1/2, 5/3 |    pi*I\
Gamma(5/3)* |   |         | 3*e    |
           2  1 \  8/3    |        /
------------------------------------
            3*Gamma(8/3)
$$\frac{\Gamma\left(\frac{5}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{3} \\ \frac{8}{3} \end{matrix}\middle| {3 e^{i \pi}} \right)}}{3 \Gamma\left(\frac{8}{3}\right)}$$
Упростить
Numerical answer [src] 
0.12184814570878
0.12184814570878
The graph
Integral of (x^4*(dx))/(sqrt(1+3x^3)) dx

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

    © Mister Exam – Calculator