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Solving integrals/ sqrt(y)-1/x

Integral of sqrt(y)-1/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
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9
$$\int\limits_{9}^{1} \left(\sqrt{y} - \frac{1}{x}\right)\, dx$$ 
Integral(sqrt(y) - 1/x, (x, 9, 1))
Detail solution

  1. Integrate term-by-term:

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

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

      1. The integral of is .

      So, the result is:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                     
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 | |\/ y  - -| dx = C - log(x) + x*\/ y 
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$$\int \left(\sqrt{y} - \frac{1}{x}\right)\, dx = C + x \sqrt{y} - \log{\left(x \right)}$$
Simplify
The answer [src] 
      ___         
- 8*\/ y  + log(9)
$$- 8 \sqrt{y} + \log{\left(9 \right)}$$ 
=
= 
      ___         
- 8*\/ y  + log(9)
$$- 8 \sqrt{y} + \log{\left(9 \right)}$$ 
-8*sqrt(y) + log(9)

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

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