ATLASBetaSearch subjects

Subjects

Ancient HistoryComing soon

Biology Business Studies

ChemistryComing soon

EngineeringComing soon

English Advanced English Ext 1 English Standard

English StudiesComing soon

Enterprise ComputingComing soon

Health & MovementComing soon

Legal Studies Maths Advanced Mathematics Ext 1 Mathematics Ext 2

Maths Standard 1Coming soon

Maths Standard 2Coming soon

Modern HistoryComing soon

Physics Religion I Religion II

Visual ArtsComing soon

Save your favourites

Accounts and progress tracking are coming later.

Coming later

2022 Mathematics Extension 2 Q12 (c) (ii) | HSC Atlas

← Back to Mathematics Extension 2 questions

2022TrialShort answer

Q12 (c) (ii)

2 marks

Question

Hence find
$\int\frac{-7x-18}{(x-1)(x^2+4)}\,dx.$

Try the question before revealing the answer.

Solution

$\int\frac{-7x-18}{(x-1)(x^2+4)}\,dx=-5\ln(x-1)+\frac52\ln(x^2+4)-\tan^{-1}\left(\frac{x}{2}\right)+C$

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Calculus

Further IntegrationApply substitution, partial fractions, integration by parts and recurrence relationships to theoretical and practical problems.

Source

Girraween 2022 4U Trial PaperGirraweenQuestion paper page 7Guidance page 16View original source ↗

Spot a problem? Send feedback

WebsiteWhat needs attention?Tell us what looks wrong

Please do not include your name, school, or other personal details.