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Integral of d{x}:
Integral of 1÷x
Integral of x^2/(1+x^3)
Integral of x^(33/10)/5
Integral of 6^x
Identical expressions
x^(thirty-three / ten)/ five
x to the power of (33 divide by 10) divide by 5
x to the power of (thirty minus three divide by ten) divide by five
x(33/10)/5
x33/10/5
x^33/10/5
x^(33 divide by 10) divide by 5
x^(33/10)/5dx

Solving integrals/ x^(33/10)/5

Integral of x^(33/10)/5 dx

The solution

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$$\int\limits_{0}^{1} \frac{x^{\frac{33}{10}}}{5}\, dx$$

Integral(x^(33/10)/5, (x, 0, 1))

Detail solution

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

$\int \frac{x^{\frac{33}{10}}}{5}\, dx = \frac{\int x^{\frac{33}{10}}\, dx}{5}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{\frac{33}{10}}\, dx = \frac{10 x^{\frac{43}{10}}}{43}$
So, the result is: $\frac{2 x^{\frac{43}{10}}}{43}$
Add the constant of integration:

$\frac{2 x^{\frac{43}{10}}}{43}+ \mathrm{constant}$

The answer is:

$\frac{2 x^{\frac{43}{10}}}{43}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |                   
 |  33             43
 |  --             --
 |  10             10
 | x            2*x  
 | --- dx = C + -----
 |  5             43 
 |                   
/

$$\int \frac{x^{\frac{33}{10}}}{5}\, dx = C + \frac{2 x^{\frac{43}{10}}}{43}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

2/43

$$\frac{2}{43}$$

2/43

$$\frac{2}{43}$$

2/43

Numerical answer [src]

0.0465116279069767

0.0465116279069767

The graph

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

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Identical expressions

Integral of x^(33/10)/5 dx

Limits of integration:

The graph:

Piecewise:

The solution