smc-748-30-Log (indefinite)

Calculus, MET1 2005 ADV 2ci

Find the value of `int (6x^2)/(x^3 + 1)\ dx`. (2 marks)

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`2\ ln\ |(x^3 + 1)| + c`

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`int (6x^2)/(x^3 + 1)\ dx`	`= 2 int (3x^2)/(x^3 + 1)\ dx`
	`= 2 ln\ \| (x^3 + 1) \| + c`

Calculus, MET1 2009 VCAA 2a

Find an anti-derivative of `1/(1 - 2x)` with respect to `x`. (2 marks)

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`-1/2 log_e | 1 – 2x |`

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`int (1 – 2x)^-1\ dx = -1/2 log_e | 1 – 2x |`

Calculus, MET1 2011 VCAA 2a

Find an antiderivative of `1/(3x - 4)` with respect to `x.` (1 mark)

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`1/3 log_e | 3x – 4 |`

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`int (3x – 4)^-1\ dx`

♦ Mean mark 43%.
MARKER’S COMMENT: The constant `c` is required for the general derivative `int f(x)\ dx` but is not necessary for an antiderivative.

`= 1/3 log_e (| 3x – 4 |)+c`