Tabelle einiger Grundintegrale
Z
xn dx= xn+1
n+ 1 +c (n6= −1, n ∈ Z, f¨ur n < −1 ist x 6= 0) Z
xα dx = xα+1
α + 1 +c (α 6= −1, α ∈ R, x > 0) Z dx
x =
lnx+c f¨ur x > 0 ln(−x) +c f¨ur x < 0
= ln|x|+c (x 6= 0) Z
ax dx = ax
lna +c (a > 0, a 6= 1) Z
cosx dx = sinx+c Z
sinx dx = −cosx+ c Z dx
cos2x = tanx+c (x 6= π2 +kπ, k ∈ Z) Z dx
sin2x = −cotx+c (x 6= kπ, k ∈ Z Z
coshx dx = sinhx+c Z
sinhx dx = coshx+c Z dx
cosh2x = tanhx+c Z dx
sinh2x = −cothx+c (x 6= 0) Z dx
√1−x2 = arcsinx+c (|x| < 1) Z dx
1 +x2 = arctanx+ c Z dx
√1 +x2 = ln(x+p
1 +x2) +c Z dx
√x2 −1 = ln|x+p
x2 −1|+c (|x| > 1) Z dx
1−x2 = 1 2ln
¯¯
¯¯x+ 1 x−1
¯¯
¯¯+c (|x| 6= 1)
