How to integrate (2x)(3-x)^-1) C4 integration

Make it ((3-X)^-1)(2x) and integrate by parts? That's how I'd do it I think lol?

Dont think its a log so

Reply 4

Zacken

22

Original post by RonnieRJ

Make it ((3-X)^-1)(2x) and integrate by parts? That's how I'd do it I think lol?

Dont think its a log so

You've just re-written the integrand with the brackets in opposite places, and integration by parts is not a viable approach here.

There is a logarithmic term in the evaluation...

Reply 5

Zacken

22

Original post by family'sfailure

(2x)(3-x)^-1

\displaystyle - 2\frac{x}{x-3} = -2 \left(\frac{x-3 + 3}{x-3}\right) = -2 \left(1 + \frac{3}{x-3}\right)

Reply 6

(2x)(3-x)^-1

Original post by alow

Try partial fractions.

If 2x/(3-x), how can that be decomposed?

I would write

\dfrac{2x}{3-x}

as

\dfrac{-(6-2x)}{3-x}+\dfrac{6}{3-x}

Reply 7

Original post by Zacken

You've just re-written the integrand with the brackets in opposite places, and integration by parts is not a viable approach here.

There is a logarithmic term in the evaluation...

Yeah exactly, so that you don't have to try and raise the power of the bracket by one

And oh whoops didn't look at it that way

Reply 8

Zacken

22

Original post by RonnieRJ

Yeah exactly, so that you don't have to try and raise the power of the bracket by one

What...?

Reply 9

Original post by Zacken

What...?

Dw it works in my head lmao I appreciate you'd do it differently

Original post by Kvothe the arcane

(2x)(3-x)^-1

If 2x/(3-x), how can that be decomposed?

I would write

\dfrac{2x}{3-x}

as

\dfrac{-(6-2x)}{3-x}+\dfrac{6}{3-x}

\dfrac{6}{3-x} -2

Reply 11

Original post by RonnieRJ

Dw it works in my head lmao I appreciate you'd do it differently

No

Reply 12

Original post by Kvothe the arcane

No

No?

Reply 13

Original post by alow

\dfrac{6}{3-x} -2

Yes

. Sorry! I phrased my question wrongly.

Is the above also considered partial fractions? I thought that partial fraction decomposition was concerned with the decomposition of fractions with algebraic denominators of order 2 or above.

(edited 8 years ago)

Reply 14