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Integral of 1/x+x^2ln5 dx

Limits of integration:

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Piecewise:

The solution

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01(x2log(5)+11x)dx\int\limits_{0}^{1} \left(x^{2} \log{\left(5 \right)} + 1 \cdot \frac{1}{x}\right)\, dx
Integral(1/x + x^2*log(5), (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:

      x2log(5)dx=log(5)x2dx\int x^{2} \log{\left(5 \right)}\, dx = \log{\left(5 \right)} \int x^{2}\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

        x2dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

      So, the result is: x3log(5)3\frac{x^{3} \log{\left(5 \right)}}{3}

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

      But the integral is

      log(x)\log{\left(x \right)}

    The result is: x3log(5)3+log(x)\frac{x^{3} \log{\left(5 \right)}}{3} + \log{\left(x \right)}

  2. Add the constant of integration:

    x3log(5)3+log(x)+constant\frac{x^{3} \log{\left(5 \right)}}{3} + \log{\left(x \right)}+ \mathrm{constant}


The answer is:

x3log(5)3+log(x)+constant\frac{x^{3} \log{\left(5 \right)}}{3} + \log{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                             
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 | /  1    2       \          x *log(5)         
 | |1*- + x *log(5)| dx = C + --------- + log(x)
 | \  x            /              3             
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logx+log5x33\log x+{{\log 5\,x^3}\over{3}}
The answer [src]
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Numerical answer [src]
44.6269254381376
44.6269254381376

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