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Solving integrals/ y/x

Integral of y/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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∫01yx dx\int\limits_{0}^{1} \frac{y}{x}\, dx 
Integral(y/x, (x, 0, 1))
Detail solution

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

    ∫yx dx=y∫1x dx\int \frac{y}{x}\, dx = y \int \frac{1}{x}\, dx

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

    So, the result is: ylog⁡(x)y \log{\left(x \right)}

  2. Add the constant of integration:

    ylog⁡(x)+constanty \log{\left(x \right)}+ \mathrm{constant}

The answer is:

ylog⁡(x)+constanty \log{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫yx dx=C+ylog⁡(x)\int \frac{y}{x}\, dx = C + y \log{\left(x \right)}
Simplify
The answer [src] 
oo*sign(y)
∞sign⁡(y)\infty \operatorname{sign}{\left(y \right)} 
=
= 
oo*sign(y)
∞sign⁡(y)\infty \operatorname{sign}{\left(y \right)} 
oo*sign(y)

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

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