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Integral of (3/sqrt(x))+4/(x^8) dx

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The solution

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 |  /  3     4 \   
 |  |----- + --| dx
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01(4x8+3x)dx\int\limits_{0}^{1} \left(\frac{4}{x^{8}} + \frac{3}{\sqrt{x}}\right)\, dx
Integral(3/sqrt(x) + 4/x^8, (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:

      4x8dx=41x8dx\int \frac{4}{x^{8}}\, dx = 4 \int \frac{1}{x^{8}}\, dx

      1. Don't know the steps in finding this integral.

        But the integral is

        17x7- \frac{1}{7 x^{7}}

      So, the result is: 47x7- \frac{4}{7 x^{7}}

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

      3xdx=31xdx\int \frac{3}{\sqrt{x}}\, dx = 3 \int \frac{1}{\sqrt{x}}\, dx

      1. Let u=xu = \sqrt{x}.

        Then let du=dx2xdu = \frac{dx}{2 \sqrt{x}} and substitute 2du2 du:

        2du\int 2\, du

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

          False\text{False}

          1. The integral of a constant is the constant times the variable of integration:

            1du=u\int 1\, du = u

          So, the result is: 2u2 u

        Now substitute uu back in:

        2x2 \sqrt{x}

      So, the result is: 6x6 \sqrt{x}

    The result is: 6x47x76 \sqrt{x} - \frac{4}{7 x^{7}}

  2. Now simplify:

    2(21x1522)7x7\frac{2 \left(21 x^{\frac{15}{2}} - 2\right)}{7 x^{7}}

  3. Add the constant of integration:

    2(21x1522)7x7+constant\frac{2 \left(21 x^{\frac{15}{2}} - 2\right)}{7 x^{7}}+ \mathrm{constant}


The answer is:

2(21x1522)7x7+constant\frac{2 \left(21 x^{\frac{15}{2}} - 2\right)}{7 x^{7}}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                    
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 | /  3     4 \              ___    4  
 | |----- + --| dx = C + 6*\/ x  - ----
 | |  ___    8|                       7
 | \\/ x    x /                    7*x 
 |                                     
/                                      
(4x8+3x)dx=C+6x47x7\int \left(\frac{4}{x^{8}} + \frac{3}{\sqrt{x}}\right)\, dx = C + 6 \sqrt{x} - \frac{4}{7 x^{7}}
The graph
0.001.000.100.200.300.400.500.600.700.800.901e33-5e32
The answer [src]
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Numerical answer [src]
2.72353730166202e+133
2.72353730166202e+133

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