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Identical expressions
(one /x)+y*exp(x)
(1 divide by x) plus y multiply by exponent of (x)
(one divide by x) plus y multiply by exponent of (x)
(1/x)+yexp(x)
1/x+yexpx
(1 divide by x)+y*exp(x)
(1/x)+y*exp(x)dx
Similar expressions
(1/x)-y*exp(x)

Integral of (1/x)+y*exp(x) dx

The solution

You have entered [src]

  1              
  /              
 |               
 |  /1      x\   
 |  |- + y*e | dx
 |  \x       /   
 |               
/                
0

$$\int\limits_{0}^{1} \left(y e^{x} + \frac{1}{x}\right)\, dx$$

Integral(1/x + y*exp(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int y e^{x}\, dx = y \int e^{x}\, dx$
  1. The integral of the exponential function is itself.
    
    $\int e^{x}\, dx = e^{x}$
  So, the result is: $y e^{x}$
1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
The result is: $y e^{x} + \log{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                 
 |                                  
 | /1      x\             x         
 | |- + y*e | dx = C + y*e  + log(x)
 | \x       /                       
 |                                  
/

$$\int \left(y e^{x} + \frac{1}{x}\right)\, dx = C + y e^{x} + \log{\left(x \right)}$$

Simplify

The answer [src]

oo + E*y

$$e y + \infty$$

oo + E*y

$$e y + \infty$$

oo + E*y

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

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Integral of (1/x)+y*exp(x) dx

Limits of integration:

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Piecewise:

The solution