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Solving integrals/ 4*3sqrt(x)-4/x

Integral of 4*3sqrt(x)-4/x dx

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The solution

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∫01(12x−4x) dx\int\limits_{0}^{1} \left(12 \sqrt{x} - \frac{4}{x}\right)\, dx 
Integral(12*sqrt(x) - 4/x, (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:

      ∫12x dx=12∫x dx\int 12 \sqrt{x}\, dx = 12 \int \sqrt{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=2x323\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}

      So, the result is: 8x328 x^{\frac{3}{2}}

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

      ∫(−4x) dx=−4∫1x dx\int \left(- \frac{4}{x}\right)\, dx = - 4 \int \frac{1}{x}\, dx

      1. The integral of 1x\frac{1}{x} is log⁡(x)\log{\left(x \right)}.

      So, the result is: −4log⁡(x)- 4 \log{\left(x \right)}

    The result is: 8x32−4log⁡(x)8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}

  2. Add the constant of integration:

    8x32−4log⁡(x)+constant8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}+ \mathrm{constant}

The answer is:

8x32−4log⁡(x)+constant8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(12x−4x) dx=C+8x32−4log⁡(x)\int \left(12 \sqrt{x} - \frac{4}{x}\right)\, dx = C + 8 x^{\frac{3}{2}} - 4 \log{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-5000050000
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
-168.361784535972
-168.361784535972

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

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