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ey 2 7 THE INDEFINITE INTEGRAL GRID Functions Simple Power Rule fr adc c [aac siny +C sins +€ hy [eter a Ide a Isexxdy Bu sexx dx eu fipin ade Buy foosect vex Zin [Seexcot sd | Bu, Jeosee x cot x dx df re tan'x+€ cost x +0 | log k* +c Log Base Jide togil+¢ Exp. Vibe fotdr = = + . nen © & zero width aa™™= “= 4¢ +a (avd units intraction) © & even split © tan x4 C e+e log |x|4C ar “_+Ca>0ael / Integration by Parts Let. [/flridx = a(b - b- fin bold ILATE MATCHMAKING GUIDE! #% Inverse = laute hierarchy Log — lems to pore above) Algebraic > Trig avoid or tram Trig + Examples... Exponential sig* Boss Level: JeY)+f@ldx=e'f@)+C . Example: Jetix) +f) Idx = e*f(x) +c | #StudyGram #EnglishHacks #ExamPrep #CalculusGlowUp #IntegralsMindMap © 4 even adntiral © © odd/even &. ——— PECIAL ie \ . FORMULAE THE re + Substitution! (5) | fata zal sal*¢ (ii) IS (in) (fx 3. Formofthe No. rational function 1 —A*E aap (x= a){e—6) =qi = tog | Fall* ae ge = logis +|x?—x1+C Form of the partial fraction A B + x=" 5-5 preg _A,# " (x-a)? (x-a) (x-aP pe tgetr ae eae, woe (x=a)(x - b){x=c) (x-a) (x-6) (x-¢) pxtt+ge +r AS eae one fr-at@-n) | FH) Gea 2) Br+C res pet tge tr A —_———— | —-+ Gall? +bx+c) | O48) © (=) limits switch te) © © odd/even split 4 © @ odd/even split 4 © Cr. odd-repats -m ax x7 + bs + + cannot be factorited further. ~» INTEGRALS: The Vibe Check | The Master Mind Map for your Math Glow-Up & “/ b Definite Integral [ f(x)dx PRO TIPS: Definite Properties! . log ||x|| +c flac x atdx =——+C loga King’s Rule és) [[flade= [’fa-xex Zero Width © [(fldax=0 STANDARD SUB FORMULAE ee + franx feotx fisec x fcosec x > INTEGR PARTIAL FR | Fraction Parting Fails? Fix it! = (G) No Repeats ve ral ~ bogs alec Ej Repeat One 3 Vo? va? +2 bags (Feat) ec (up Repeat -SygF-aFa Sons 4c Non-linear W Page 12 
