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Identical expressions
pi(x^ four +6x^ two + nine)dx
Pi (x to the power of 4 plus 6x squared plus 9)dx
Pi (x to the power of four plus 6x to the power of two plus nine)dx
pi(x4+6x2+9)dx
pix4+6x2+9dx
pi(x⁴+6x²+9)dx
pi(x to the power of 4+6x to the power of 2+9)dx
pix^4+6x^2+9dx
Similar expressions
pi(x^4-6x^2+9)dx
pi(x^4+6x^2-9)dx

Integral of pi(x^4+6x^2+9)dx dx

The solution

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  1                      
  /                      
 |                       
 |     / 4      2    \   
 |  pi*\x  + 6*x  + 9/ dx
 |                       
/                        
0

$$\int\limits_{0}^{1} \pi \left(\left(x^{4} + 6 x^{2}\right) + 9\right)\, dx$$

Integral(pi*(x^4 + 6*x^2 + 9), (x, 0, 1))

Detail solution

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

$\int \pi \left(\left(x^{4} + 6 x^{2}\right) + 9\right)\, dx = \pi \int \left(\left(x^{4} + 6 x^{2}\right) + 9\right)\, dx$
1. Integrate term-by-term:
  1. Integrate term-by-term:
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{4}\, dx = \frac{x^{5}}{5}$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int 6 x^{2}\, dx = 6 \int x^{2}\, dx$
      1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
        
        $\int x^{2}\, dx = \frac{x^{3}}{3}$
      So, the result is: $2 x^{3}$
    The result is: $\frac{x^{5}}{5} + 2 x^{3}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 9\, dx = 9 x$
  The result is: $\frac{x^{5}}{5} + 2 x^{3} + 9 x$
So, the result is: $\pi \left(\frac{x^{5}}{5} + 2 x^{3} + 9 x\right)$
Now simplify:

$\frac{\pi x \left(x^{4} + 10 x^{2} + 45\right)}{5}$
Add the constant of integration:

$\frac{\pi x \left(x^{4} + 10 x^{2} + 45\right)}{5}+ \mathrm{constant}$

The answer is:

$\frac{\pi x \left(x^{4} + 10 x^{2} + 45\right)}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                                /              5\
 |    / 4      2    \             |   3         x |
 | pi*\x  + 6*x  + 9/ dx = C + pi*|2*x  + 9*x + --|
 |                                \             5 /
/

$$\int \pi \left(\left(x^{4} + 6 x^{2}\right) + 9\right)\, dx = C + \pi \left(\frac{x^{5}}{5} + 2 x^{3} + 9 x\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

56*pi
-----
  5

$$\frac{56 \pi}{5}$$

56*pi
-----
  5

$$\frac{56 \pi}{5}$$

56*pi/5

Numerical answer [src]

35.1858377202057

35.1858377202057

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

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Integral of pi(x^4+6x^2+9)dx dx

Limits of integration:

The graph:

Piecewise:

The solution