Integral of (x+1)e^x dx
The solution
Detail solution
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Rewrite the integrand:
ex(x+1)=xex+ex
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Integrate term-by-term:
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Use integration by parts:
∫udv=uv−∫vdu
Let u(x)=x and let dv(x)=ex.
Then du(x)=1.
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 the exponential function is itself.
∫exdx=ex
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The integral of the exponential function is itself.
∫exdx=ex
The result is: xex
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Add the constant of integration:
xex+constant
The answer is:
xex+constant
The answer (Indefinite)
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| x x
| (x + 1)*E dx = C + x*e
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∫ex(x+1)dx=C+xex
The graph
Use the examples entering the upper and lower limits of integration.