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Standardintegraler

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cobbe's version from 2016-08-18 14:37

Section

Question Answer
S (x^r) dx(x^r+1)/(r+1) + C
S (e^x) dxe^x + C
S (1/x) dxln|x| + C
S (sin(x)) dx-cos(x) + C
S (cos(x)) dxsin(x) + C
memorize

 

Question Answer
S (1/(sqrt(1-x^2))) dxarcsin(x) + C
S (-1/(sqrt(1-x^2))) dxarccos(x) + C
S (1/(1+x^2)) dxarctan(x) + C
memorize

 

Question Answer
S (a^x) dx(a^x)/(ln(a)) + C
memorize

 

Question Answer
Partialintegration (PI) = S (f(x) * g(x)) dxF(x)*g(x) - S (F(X) * g'(x)) dx
memorize
Partialbråksuppdelning (PBU) efter faktor i nämnaren, används genom att vänsterled ska vara lika med högerled
Question Answer
x+aA / (x+a)
(x+a)^nA1 / (x+a) + A2 / (x+a)^2 + ... + An / (x+a)^n
(x^2 + ax + b)(Ax + B) / (x^2 + ax + b)
(x^2 + ax + b)^n(A1x + B1) / (x^2 + ax + b) + (A2x + B2) / (x^2 + ax + b)^2 + ... + (An*x + Bn) / (x^2 + ax + b)^n
memorize

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