integration through substitution Watch

one-final-hit
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#1
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#1
Ive been asked to integrate
f(x)=(x^3) * (4+x^2)^(-1/2)

using u = 4 + x^2 as substitution.

I'm unable to identify which substitution [direct or reverse] to use.
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Potassium^2
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#2
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? It tells you the substitution to use
Find du/dx also to change the variable of the integral
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one-final-hit
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(Original post by Potassium^2)
? It tells you the substitution to use
Find du/dx also to change the variable of the integral
du/dx = 2x, problem is I can't fit it into the equation... [having already substituted u for x).
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Potassium^2
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#4
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Ah I see what you mean
have a look here: http://www.wolframalpha.com/input/?i...x%5E2%29%29%5D
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BJack
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(Original post by one-final-hit)
du/dx = 2x, problem is I can't fit it into the equation... [having already substituted u for x).
You can rewrite \displaystyle\frac{x^3}{\sqrt{4+  x^2}}\ \mathrm{d}x as \displaystyle\frac{\frac{1}{2}x^  2}{\sqrt{4+x^2}}\ 2x\mathrm{d}x.

Does that help you see how to fit everything in?
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Farhan.Hanif93
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#6
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(Original post by one-final-hit)
du/dx = 2x, problem is I can't fit it into the equation... [having already substituted u for x).
Note that f(x) = 2x \times \dfrac{x^2}{2\sqrt{4+x^2}}. If you consider the integral of this and use the substitution, it should be clear how this substitution can be fully applied to f(x).

EDIT: BJack is too fast. :p:
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one-final-hit
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#7
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Cheers guys, I think I can take it from here
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