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Similar expressions
(x^3-x^(3/4))

Solving integrals/ (x^3+x^(3/4))

Integral of (x^3+x^(3/4)) dx

The solution

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  4               
  /               
 |                
 |  / 3    3/4\   
 |  \x  + x   / dx
 |                
/                 
1

$$\int\limits_{1}^{4} \left(x^{\frac{3}{4}} + x^{3}\right)\, dx$$

Integral(x^3 + x^(3/4), (x, 1, 4))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{\frac{3}{4}}\, dx = \frac{4 x^{\frac{7}{4}}}{7}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
The result is: $\frac{4 x^{\frac{7}{4}}}{7} + \frac{x^{4}}{4}$
Add the constant of integration:

$\frac{4 x^{\frac{7}{4}}}{7} + \frac{x^{4}}{4}+ \mathrm{constant}$

The answer is:

$\frac{4 x^{\frac{7}{4}}}{7} + \frac{x^{4}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                       4      7/4
 | / 3    3/4\          x    4*x   
 | \x  + x   / dx = C + -- + ------
 |                      4      7   
/

$${{x^4}\over{4}}+{{4\,x^{{{7}\over{4}}}}\over{7}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

            ___
1769   32*\/ 2 
---- + --------
 28       7

$${{2^{{{15}\over{2}}}+1769}\over{28}}$$

            ___
1769   32*\/ 2 
---- + --------
 28       7

$$\frac{32 \sqrt{2}}{7} + \frac{1769}{28}$$

Упростить

Numerical answer [src]

69.6435477137056

69.6435477137056

The graph

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

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Integral of (x^3+x^(3/4)) dx

Limits of integration:

The graph:

Piecewise:

The solution