Integral of (x+2)^2dx dx
The solution
Detail solution
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There are multiple ways to do this integral.
Method #1
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Let u=x+2.
Then let du=dx and substitute du:
∫u2du
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The integral of un is n+1un+1 when n=−1:
∫u2du=3u3
Now substitute u back in:
3(x+2)3
Method #2
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Rewrite the integrand:
(x+2)2=x2+4x+4
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Integrate term-by-term:
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The integral of xn is n+1xn+1 when n=−1:
∫x2dx=3x3
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The integral of a constant times a function is the constant times the integral of the function:
∫4xdx=4∫xdx
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The integral of xn is n+1xn+1 when n=−1:
∫xdx=2x2
So, the result is: 2x2
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The integral of a constant is the constant times the variable of integration:
∫4dx=4x
The result is: 3x3+2x2+4x
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Now simplify:
3(x+2)3
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Add the constant of integration:
3(x+2)3+constant
The answer is:
3(x+2)3+constant
The answer (Indefinite)
[src]
/
| 3
| 2 (x + 2)
| (x + 2) dx = C + --------
| 3
/
∫(x+2)2dx=C+3(x+2)3
The graph
Use the examples entering the upper and lower limits of integration.