L10 Strategy of Integration - csc x ln j sec x tan x j c 4 ex Z arctan x x 2 dx arctan x x ln j x j 1 2 ln(1 x 2 c 5 ex Z p x 1 x 3 dx 2 3 arctan x 3 2

# L10 Strategy of Integration - csc x ln j sec x tan x j c 4...

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Lecture 10:Review:Strategy of Inte-grationex.Z1xp4x2+ 1dx[](lnjp4x2+12x12xj+c)ex.Zdx(1x2)3=2[](xp1x2+c)1
Strategy for integration:1. Simplify the integrand if possible;making sure rational expression isproper.2. Look for obvioussubstitution.3. Iff(x) is a product of a polynomial and atranscendental function(trig, exponential, logarith-mic), tryby parts.4.Iff(x) is a product of powers of sinxandcosx, of tanxand secx, or of cotxand cscx,then we use the rules fortrig. integration.5. Iff(x) is a rational function,trypartial fraction.6. Ifpa2x2b2occurs,try trig.sub; ifnpg(x)occurs, rationalize it by using au-sub.7. Sometimes, you need to manipulate theintegrand.8. Use several methods. Try and try.2
ex.Zsin3xcosxdx[](cos2x2lnjcosxj+c)3
ex.Zsec3xtan2xdx[]