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Solving integrals/ dx/(sqrt(x)+3sqrt(x))

Integral of dx/(sqrt(x)+3sqrt(x)) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

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∫001x+3x dx\int\limits_{0}^{0} \frac{1}{\sqrt{x} + 3 \sqrt{x}}\, dx 
Integral(1/(sqrt(x) + 3*sqrt(x)), (x, 0, 0))
Detail solution

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

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

    ∫12 du\int \frac{1}{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:

        ∫1 du=u\int 1\, du = u

      So, the result is: u2\frac{u}{2}

    Now substitute uu back in:

    x2\frac{\sqrt{x}}{2}

  2. Add the constant of integration:

    x2+constant\frac{\sqrt{x}}{2}+ \mathrm{constant}

The answer is:

x2+constant\frac{\sqrt{x}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫1x+3x dx=C+x2\int \frac{1}{\sqrt{x} + 3 \sqrt{x}}\, dx = C + \frac{\sqrt{x}}{2}
Simplify
The graph
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    Use the examples entering the upper and lower limits of integration.

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