Integral of y/x dx

You have entered [src]

$$\int\limits_{0}^{1} \frac{y}{x}\, dx$$

Integral(y/x, (x, 0, 1))

Detail solution

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

$\int \frac{y}{x}\, dx = y \int \frac{1}{x}\, dx$
1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
So, the result is: $y \log{\left(x \right)}$
Add the constant of integration:

$y \log{\left(x \right)}+ \mathrm{constant}$

The answer is:

$y \log{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                   
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 | y                  
 | - dx = C + y*log(x)
 | x                  
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/

$$\int \frac{y}{x}\, dx = C + y \log{\left(x \right)}$$

Simplify

The answer [src]

oo*sign(y)

$$\infty \operatorname{sign}{\left(y \right)}$$

oo*sign(y)

$$\infty \operatorname{sign}{\left(y \right)}$$

oo*sign(y)

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