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# step by step of how to find the antiderivative of "3 ln x" ?

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step by step of how to find the antiderivative of "3 ln x" ?

Apr 24, 2015

#1
+99272
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You do this with integration by parts

f(x)=lnx                    g'(x)=3

f'(x)=1/x                   g(x)=3x

$$\\\boxed{\int\;f(x)g'(x)dx=f(x)g(x)-\int\;g(x)f'(x)dx}\\\\\\\\ \int\;((lnx)*3)dx\\\\ =(lnx)(3x)-\int\;(3x*\frac{1}{x})dx\\\\ =(3xlnx)-\int\;(3)dx\\\\ =(3xlnx)-3x+c\\\\ =3x(ln(x)-1)+c$$

I think that my working is right but you should check it anyway :)

Apr 25, 2015

#1
+99272
+5

You do this with integration by parts

f(x)=lnx                    g'(x)=3

f'(x)=1/x                   g(x)=3x

$$\\\boxed{\int\;f(x)g'(x)dx=f(x)g(x)-\int\;g(x)f'(x)dx}\\\\\\\\ \int\;((lnx)*3)dx\\\\ =(lnx)(3x)-\int\;(3x*\frac{1}{x})dx\\\\ =(3xlnx)-\int\;(3)dx\\\\ =(3xlnx)-3x+c\\\\ =3x(ln(x)-1)+c$$