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Integral of d{x}:
Integral of 0dx
Integral of x*cos(x/2)
Integral of (x-2)^2dx
Integral of x/(2*x+1)
Derivative of:
(x+1)e^x
Identical expressions
(x+ one)e^x
(x plus 1)e to the power of x
(x plus one)e to the power of x
(x+1)ex
x+1ex
x+1e^x
(x+1)e^xdx
Similar expressions
(x-1)e^x
(3x+1)e^x

Solving integrals/ (x+1)e^x

Integral of (x+1)e^x dx

The solution

You have entered [src]

  1              
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 |  (x + 1)*E  dx
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0

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

Integral((x + 1)*E^x, (x, 0, 1))

Detail solution

Rewrite the integrand:

$e^{x} \left(x + 1\right) = x e^{x} + e^{x}$
Integrate term-by-term:
1. Use integration by parts:
  
  $\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}$
  
  Let $u{\left(x \right)} = x$ and let $\operatorname{dv}{\left(x \right)} = e^{x}$ .
  
  Then $\operatorname{du}{\left(x \right)} = 1$ .
  
  To find $v{\left(x \right)}$ :
  1. The integral of the exponential function is itself.
    
    $\int e^{x}\, dx = e^{x}$
  Now evaluate the sub-integral.
2. The integral of the exponential function is itself.
  
  $\int e^{x}\, dx = e^{x}$
1. The integral of the exponential function is itself.
  
  $\int e^{x}\, dx = e^{x}$
The result is: $x e^{x}$
Add the constant of integration:

$x e^{x}+ \mathrm{constant}$

The answer is:

$x e^{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                         
 |          x             x
 | (x + 1)*E  dx = C + x*e 
 |                         
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$e$$

=

$$e$$

Numerical answer [src]

2.71828182845905

2.71828182845905

The graph

Integral of (x+1)e^x dx

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