Integral of ((2/x)+4x^(-3/2)) dx
The solution
Detail solution
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Integrate term-by-term:
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The integral of a constant times a function is the constant times the integral of the function:
∫x2dx=2∫x1dx
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The integral of x1 is log(x).
So, the result is: 2log(x)
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The integral of a constant times a function is the constant times the integral of the function:
∫x234dx=4∫x231dx
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The integral of xn is n+1xn+1 when n=−1:
∫x231dx=−x2
So, the result is: −x8
The result is: 2log(x)−x8
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Add the constant of integration:
2log(x)−x8+constant
The answer is:
2log(x)−x8+constant
The answer (Indefinite)
[src]
/
|
| /2 4 \ 8
| |- + ----| dx = C - ----- + 2*log(x)
| |x 3/2| ___
| \ x / \/ x
|
/
∫(x2+x234)dx=C+2log(x)−x8
The graph
___
___ 8*\/ 3
-2*log(2) + 2*log(3) + 4*\/ 2 - -------
3
−383−2log(2)+2log(3)+42
=
___
___ 8*\/ 3
-2*log(2) + 2*log(3) + 4*\/ 2 - -------
3
−383−2log(2)+2log(3)+42
-2*log(2) + 2*log(3) + 4*sqrt(2) - 8*sqrt(3)/3
Use the examples entering the upper and lower limits of integration.