Tabla de integrales

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Tabla de Derivadas e Integrales Función y=c y = c.x y = xn y=xn y = x½ y = xa/b y = 1/x y = sen x y = cos x y = tg x y = cotg x y = secx y = cosec x y = arcsen x y = arccos x y = arctg x y = arccotg x y = arcsec x y = arccosec x y = senh x y = cosh x y = tgh x y = cotghx y = sech x y = cosech x y = ln x y = logax y=e
x

Dervada y' = 0 y' = c y' = n.xn-1 y’ = -1/(n.xn-1) y’ = 1/(2.x½) y' =a.x(a/b)-1/b y' = -1/x2 y' = cos x y' = -sen x y' = 1/cos x y' = -1/sen x y' = sen x/cos x y' = -cos x/sen x y' = 1/(1 - x )
2 ½ 2 2 2 2Integral c.x c.x2/2 xn+1/n+1 x-n+1/-n+1 2.x3/2/3 x(a/b)+1/[(a/b)+1] ln x -cos x sen x -ln cos x ln sen x ln (tg ½.x) ln [cos x/(1 - sen x)]x.arcsen x + (1 - x2)½ x.arccos x - (1 - x2)½ x.arctg x - ½ln (1 + x2) x.arccotg x + ½ln (1 + x2) 1

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y' = -1/(1 - x2)½ y' = 1/(1 +x2) y' = -1/(1 + x2) y' = 1/[x.(x2 -1)½] y' = -1/[x.(x – 1) ] y' = cosh x y' = senh x y' = sech x y' = -cosech x y' = -sech x.tgh x y'= -cosech x.cotgh x y' = 1/x y' = 1/x.ln a y' = e
x 2 2 2 ½

2 cosh x senh x ln cosh x ln senh x 3 4 x.(ln x - 1) x.( logax - 1/ln a)ex ax/ln a 5 6

y = ax y = xx y=e
u

y' = ax.ln a y' = xx.(ln x + 1) y’ = e .u’ y' = u'.v + v'.u y' = (u'.v - v'.u)/v
2 u

y =u.v y = u/v y = uv

∫u.dv + ∫v.du
7 8

y' = uv.(v'.lnu + v.u'/u)

y = lnuv

y’ = (v’.u.lnu - u’.v.lnv)/v.u.ln2u

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