Mister Exam

Other calculators

Solving integrals/ xe^x-(y/x^2)

Integral of xe^x-(y/x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x               
  /               
 |                
 |  /   x   y \   
 |  |x*E  - --| dx
 |  |        2|   
 |  \       x /   
 |                
/                 
0
$$\int\limits_{0}^{x} \left(e^{x} x - \frac{y}{x^{2}}\right)\, dx$$ 
Integral(x*E^x - y/x^2, (x, 0, x))
Detail solution

  1. Integrate term-by-term:

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

      But the integral is

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

        PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=0, context=1/(x**2), symbol=x), False), (ArccothRule(a=1, b=1, c=0, context=1/(x**2), symbol=x), False), (ArctanhRule(a=1, b=1, c=0, context=1/(x**2), symbol=x), False)], context=1/(x**2), symbol=x)

      So, the result is:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                    
 |                     
 | /   x   y \         
 | |x*E  - --| dx = nan
 | |        2|         
 | \       x /         
 |                     
/
$$\int \left(e^{x} x - \frac{y}{x^{2}}\right)\, dx = \text{NaN}$$
Simplify
The answer [src] 
              y             x
-oo*sign(y) + - + (-1 + x)*e 
              x
$$\left(x - 1\right) e^{x} - \infty \operatorname{sign}{\left(y \right)} + \frac{y}{x}$$ 
=
= 
              y             x
-oo*sign(y) + - + (-1 + x)*e 
              x
$$\left(x - 1\right) e^{x} - \infty \operatorname{sign}{\left(y \right)} + \frac{y}{x}$$ 
-oo*sign(y) + y/x + (-1 + x)*exp(x)

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

    © Mister Exam – Calculator