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Integral of x^3*e^x dx
The solution
Detail solution
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Use integration by parts:
∫udv=uv−∫vdu
Let u(x)=x3 and let dv(x)=ex.
Then du(x)=3x2.
To find v(x):
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The integral of the exponential function is itself.
∫exdx=ex
Now evaluate the sub-integral.
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Use integration by parts:
∫udv=uv−∫vdu
Let u(x)=3x2 and let dv(x)=ex.
Then du(x)=6x.
To find v(x):
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The integral of the exponential function is itself.
∫exdx=ex
Now evaluate the sub-integral.
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Use integration by parts:
∫udv=uv−∫vdu
Let u(x)=6x and let dv(x)=ex.
Then du(x)=6.
To find v(x):
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The integral of the exponential function is itself.
∫exdx=ex
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:
∫6exdx=6∫exdx
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The integral of the exponential function is itself.
∫exdx=ex
So, the result is: 6ex
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Now simplify:
(x3−3x2+6x−6)ex
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Add the constant of integration:
(x3−3x2+6x−6)ex+constant
The answer is:
(x3−3x2+6x−6)ex+constant
The answer (Indefinite)
[src]
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| 3 x x 3 x 2 x x
| x *e dx = C - 6*e + x *e - 3*x *e + 6*x*e
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(x3−3x2+6x−6)ex
The graph
Use the examples entering the upper and lower limits of integration.