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4*x*exp(x^2)
Solving integrals/ 4*x*exp(x^2)

Integral of 4*x*exp(x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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 |  4*x*e     dx
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0
∫014xex2 dx\int\limits_{0}^{1} 4 x e^{x^{2}}\, dx 
Integral((4*x)*exp(x^2), (x, 0, 1))
Detail solution

  1. Let u=x2u = x^{2}.

    Then let du=2xdxdu = 2 x dx and substitute 2du2 du:

    ∫2eu du\int 2 e^{u}\, du

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

      False\text{False}

      1. The integral of the exponential function is itself.

        ∫eu du=eu\int e^{u}\, du = e^{u}

      So, the result is: 2eu2 e^{u}

    Now substitute uu back in:

    2ex22 e^{x^{2}}

  2. Add the constant of integration:

    2ex2+constant2 e^{x^{2}}+ \mathrm{constant}

The answer is:

2ex2+constant2 e^{x^{2}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
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 |      / 2\             / 2\
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 | 4*x*e     dx = C + 2*e    
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∫4xex2 dx=C+2ex2\int 4 x e^{x^{2}}\, dx = C + 2 e^{x^{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90020
Plot the graph f(x)
The answer [src] 
-2 + 2*E
−2+2e-2 + 2 e 
=
= 
-2 + 2*E
−2+2e-2 + 2 e 
-2 + 2*E
Numerical answer [src] 
3.43656365691809
3.43656365691809
The graph
Integral of 4*x*exp(x^2) dx

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

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