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(12x¾-9x^5/3)dx
Solving integrals/ (12x¾-9x^5/3)dx

You entered:

(12x¾-9x^5/3)dx

What you mean?

(12*x*3/4 - 9*x^5/3)*dx
 
(12*x*3/4 - 9*x^(5/3))*dx
 
(12*x*3/4 - 9*x^(5/3))*dx

Integral of (12x¾-9x^5/3)dx dx

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Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |  /            5\   
 |  |12*x*3   9*x |   
 |  |------ - ----| dx
 |  \  4       3  /   
 |                    
/                     
0
∫01(3⋅12x4−9x53) dx\int\limits_{0}^{1} \left(\frac{3 \cdot 12 x}{4} - \frac{9 x^{5}}{3}\right)\, dx 
Integral((12*x)*3/4 - 9*x^5/3, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫3⋅12x4 dx=3∫12x dx4\int \frac{3 \cdot 12 x}{4}\, dx = \frac{3 \int 12 x\, dx}{4}

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

        ∫12x dx=12∫x dx\int 12 x\, dx = 12 \int x\, dx

        1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

          ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

        So, the result is: 6x26 x^{2}

      So, the result is: 9x22\frac{9 x^{2}}{2}

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

      ∫(−9x53) dx=−∫9x5 dx3\int \left(- \frac{9 x^{5}}{3}\right)\, dx = - \frac{\int 9 x^{5}\, dx}{3}

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

        ∫9x5 dx=9∫x5 dx\int 9 x^{5}\, dx = 9 \int x^{5}\, dx

        1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

          ∫x5 dx=x66\int x^{5}\, dx = \frac{x^{6}}{6}

        So, the result is: 3x62\frac{3 x^{6}}{2}

      So, the result is: −x62- \frac{x^{6}}{2}

    The result is: −x62+9x22- \frac{x^{6}}{2} + \frac{9 x^{2}}{2}

  2. Now simplify:

    x2(9−x4)2\frac{x^{2} \left(9 - x^{4}\right)}{2}

  3. Add the constant of integration:

    x2(9−x4)2+constant\frac{x^{2} \left(9 - x^{4}\right)}{2}+ \mathrm{constant}

The answer is:

x2(9−x4)2+constant\frac{x^{2} \left(9 - x^{4}\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                                   
 | /            5\           6      2
 | |12*x*3   9*x |          x    9*x 
 | |------ - ----| dx = C - -- + ----
 | \  4       3  /          2     2  
 |                                   
/
∫(3⋅12x4−9x53) dx=C−x62+9x22\int \left(\frac{3 \cdot 12 x}{4} - \frac{9 x^{5}}{3}\right)\, dx = C - \frac{x^{6}}{2} + \frac{9 x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
4
44 
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4
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Numerical answer [src] 
4.0
4.0
The graph
Integral of (12x¾-9x^5/3)dx dx

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

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