Integral of x^2*e^2*x dx
The solution
Detail solution
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Let u=x2.
Then let du=2xdx and substitute 2due2:
∫2ue2du
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The integral of a constant times a function is the constant times the integral of the function:
∫udu=2e2∫udu
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The integral of un is n+1un+1 when n=−1:
∫udu=2u2
So, the result is: 4u2e2
Now substitute u back in:
4x4e2
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Add the constant of integration:
4x4e2+constant
The answer is:
4x4e2+constant
The answer (Indefinite)
[src]
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| 4 2
| 2 2 x *e
| x *E *x dx = C + -----
| 4
/
∫xe2x2dx=C+4x4e2
The graph
Use the examples entering the upper and lower limits of integration.