Mister Exam

Other calculators


2*x*exp(x)

Integral of 2*x*exp(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |       x   
 |  2*x*e  dx
 |           
/            
0            
012xexdx\int\limits_{0}^{1} 2 x e^{x}\, dx
Integral((2*x)*exp(x), (x, 0, 1))
Detail solution
  1. Use integration by parts:

    udv=uvvdu\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}

    Let u(x)=2xu{\left(x \right)} = 2 x and let dv(x)=ex\operatorname{dv}{\left(x \right)} = e^{x}.

    Then du(x)=2\operatorname{du}{\left(x \right)} = 2.

    To find v(x)v{\left(x \right)}:

    1. The integral of the exponential function is itself.

      exdx=ex\int e^{x}\, dx = e^{x}

    Now evaluate the sub-integral.

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

    2exdx=2exdx\int 2 e^{x}\, dx = 2 \int e^{x}\, dx

    1. The integral of the exponential function is itself.

      exdx=ex\int e^{x}\, dx = e^{x}

    So, the result is: 2ex2 e^{x}

  3. Now simplify:

    2(x1)ex2 \left(x - 1\right) e^{x}

  4. Add the constant of integration:

    2(x1)ex+constant2 \left(x - 1\right) e^{x}+ \mathrm{constant}


The answer is:

2(x1)ex+constant2 \left(x - 1\right) e^{x}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                             
 |                              
 |      x             x        x
 | 2*x*e  dx = C - 2*e  + 2*x*e 
 |                              
/                               
2xexdx=C+2xex2ex\int 2 x e^{x}\, dx = C + 2 x e^{x} - 2 e^{x}
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1010
The answer [src]
2
22
=
=
2
22
2
Numerical answer [src]
2.0
2.0
The graph
Integral of 2*x*exp(x) dx

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