Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (1+x)/x
Integral of -15x^2
Integral of (1+x^4)^(1/2)
Integral of xcoskx
Derivative of:
e^x(x+1)
Identical expressions
e^x(x+ one)
e to the power of x(x plus 1)
e to the power of x(x plus one)
ex(x+1)
exx+1
e^xx+1
e^x(x+1)dx
Similar expressions
e^x(x-1)

Solving integrals/ e^x(x+1)

Integral of e^x(x+1) dx

The solution

You have entered [src]

  1              
  /              
 |               
 |   x           
 |  E *(x + 1) dx
 |               
/                
0

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

Integral(E^x*(x + 1), (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
 | E *(x + 1) 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 e^x(x+1) dx

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