What you’ll learn6 learning objectivesChoose one objective for a focused lesson, or study the complete topic.3.5.1Extended integration rules• extend the idea of 'reverse differentiation' to include the integration of eax + b, ax b 1 +, sin(ax + b), cos(ax + b), sec2(ax + b) and xa 1 22+ Including examples such as x23 1 2+.Syllabus objective3.5.2Trig integration• use trigonometrical relationships in carrying out integration e.g. use of double-angle formulae to integrate sin2 x or cos2(2x).Syllabus objective3.5.3Partial fractions• integrate rational functions by means of decomposition into partial fractions Restricted to types of partial fractions as specified in topic 3.1 above.Syllabus objective3.5.4An integrand of the form x• recognise an integrand of the form x k x f f l ^ ^ h h, and integrate such functions e.g. integration of x x 12 +, tan x.Syllabus objective3.5.5Inverse tangent• recognise when an integrand can usefully be regarded as a product, and use integration by parts e.g. integration of x sin 2x, x2e-x, ln x, x tan-1 x.Syllabus objective3.5.6Integration by substitution• use a given substitution to simplify and evaluate either a definite or an indefinite integral. e.g. to integrate sin2 2x cos x using the substitution u = sin x.Syllabus objective