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G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Jan 11, 2011 #2 8∫1zdz=8ln(z)\displaystyle 8\int\frac{1}{z}dz=8ln(z)8∫z1dz=8ln(z) Remember, the derivative of ln(x) is 1/x. Therefore, the antiderivative of 1/x is ln(x).
8∫1zdz=8ln(z)\displaystyle 8\int\frac{1}{z}dz=8ln(z)8∫z1dz=8ln(z) Remember, the derivative of ln(x) is 1/x. Therefore, the antiderivative of 1/x is ln(x).
C CatchThis2 Junior Member Joined Feb 6, 2010 Messages 96 Jan 11, 2011 #3 I see how you got that thanks!
L lookagain Elite Member Joined Aug 22, 2010 Messages 3,258 Jan 11, 2011 #4 galactus said: 8∫1zdz=8ln(z)\displaystyle 8\int\frac{1}{z}dz=8ln(z)8∫z1dz=8ln(z) Remember, the derivative of ln(x) is 1/x. Therefore, the antiderivative of 1/x is ln(x). Click to expand... \(\displaystyle 8 \int \frac{1}{z}dz \ = \ 8 \ln|z| + \bigg C\)
galactus said: 8∫1zdz=8ln(z)\displaystyle 8\int\frac{1}{z}dz=8ln(z)8∫z1dz=8ln(z) Remember, the derivative of ln(x) is 1/x. Therefore, the antiderivative of 1/x is ln(x). Click to expand... \(\displaystyle 8 \int \frac{1}{z}dz \ = \ 8 \ln|z| + \bigg C\)