Integral of x^2/(x+2) dx
The solution
Detail solution
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Rewrite the integrand:
x+2x2=x−2+x+24
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Integrate term-by-term:
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The integral of xn is n+1xn+1 when n=−1:
∫xdx=2x2
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The integral of a constant is the constant times the variable of integration:
∫(−2)dx=−2x
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The integral of a constant times a function is the constant times the integral of the function:
∫x+24dx=4∫x+21dx
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Let u=x+2.
Then let du=dx and substitute du:
∫u1du
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The integral of u1 is log(u).
Now substitute u back in:
log(x+2)
So, the result is: 4log(x+2)
The result is: 2x2−2x+4log(x+2)
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Add the constant of integration:
2x2−2x+4log(x+2)+constant
The answer is:
2x2−2x+4log(x+2)+constant
The answer (Indefinite)
[src]
/
|
| 2 2
| x x
| ----- dx = C + -- - 2*x + 4*log(2 + x)
| x + 2 2
|
/
∫x+2x2dx=C+2x2−2x+4log(x+2)
The graph
-3/2 - 4*log(2) + 4*log(3)
−4log(2)−23+4log(3)
=
-3/2 - 4*log(2) + 4*log(3)
−4log(2)−23+4log(3)
-3/2 - 4*log(2) + 4*log(3)
Use the examples entering the upper and lower limits of integration.