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Integration By Substitution Help Please...

\int 2x\ (3x^2 + 5)^2 dx

Okay, I know u=3x^2+5 and du/dx=6x and dx/du=1/6x

How do I cancel out the 2x in the question? I cancelled 1/6x divided by 2x which equals 1/3x ? then what next? :|

Reply 1

nuodai

What you've done is say that

\dfrac{2x}{6x} = \dfrac{1}{3x}

... what's wrong with that? [Something is wrong with it.]

Say we had

x=2

. Does

\dfrac{4}{12} = \dfrac{1}{6}

?

So what might you do to make it right?

Reply 2

Nkhan

Original post by nuodai

What you've done is say that

\dfrac{2x}{6x} = \dfrac{1}{3x}

... what's wrong with that? [Something is wrong with it.]

Say we had

x=2

. Does

\dfrac{4}{12} = \dfrac{1}{6}

?

So what might you do to make it right?

is it 6x divided by 2x which will give 3

Reply 3

nuodai

Original post by Nkhan

is it 6x divided by 2x which will give 3

You're dividing 2x by 6x, not the other way round.

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Integration By Substitution Help Please...

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