Integral of x*exp(4*x) dx
The solution
Detail solution
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Use integration by parts:
∫udv=uv−∫vdu
Let u(x)=x and let dv(x)=e4x.
Then du(x)=1.
To find v(x):
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Let u=4x.
Then let du=4dx and substitute 4du:
∫4eudu
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The integral of a constant times a function is the constant times the integral of the function:
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The integral of the exponential function is itself.
∫eudu=eu
So, the result is: 4eu
Now substitute u back in:
4e4x
Now evaluate the sub-integral.
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The integral of a constant times a function is the constant times the integral of the function:
∫4e4xdx=4∫e4xdx
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Let u=4x.
Then let du=4dx and substitute 4du:
∫4eudu
-
The integral of a constant times a function is the constant times the integral of the function:
-
The integral of the exponential function is itself.
∫eudu=eu
So, the result is: 4eu
Now substitute u back in:
4e4x
So, the result is: 16e4x
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Now simplify:
16(4x−1)e4x
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Add the constant of integration:
16(4x−1)e4x+constant
The answer is:
16(4x−1)e4x+constant
The answer (Indefinite)
[src]
/
| 4*x 4*x
| 4*x e x*e
| x*e dx = C - ---- + ------
| 16 4
/
∫xe4xdx=C+4xe4x−16e4x
The graph
161+163e4
=
161+163e4
Use the examples entering the upper and lower limits of integration.