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Integral of (6sqrt(x)+3x^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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  4                    
  /                    
 |                     
 |  /    ___      2\   
 |  \6*\/ x  + 3*x / dx
 |                     
/                      
1                      
$$\int\limits_{1}^{4} \left(6 \sqrt{x} + 3 x^{2}\right)\, dx$$
Integral(6*sqrt(x) + 3*x^2, (x, 1, 4))
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:

      1. The integral of is when :

      So, the result is:

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

      1. The integral of is when :

      So, the result is:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                     
 |                                      
 | /    ___      2\           3      3/2
 | \6*\/ x  + 3*x / dx = C + x  + 4*x   
 |                                      
/                                       
$$\int \left(6 \sqrt{x} + 3 x^{2}\right)\, dx = C + 4 x^{\frac{3}{2}} + x^{3}$$
The graph
The answer [src]
91
$$91$$
=
=
91
$$91$$
91
Numerical answer [src]
91.0
91.0

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