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

Guest Apr 24, 2015

Best Answer 

 #1
avatar+92806 
+5

You do this with integration by parts 

f(x)=lnx                    g'(x)=3

f'(x)=1/x                   g(x)=3x

 

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

 

https://www.khanacademy.org/math/integral-calculus/integration-techniques/integration_by_parts/v/integral-of-ln-x

 

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

Melody  Apr 25, 2015
 #1
avatar+92806 
+5
Best Answer

You do this with integration by parts 

f(x)=lnx                    g'(x)=3

f'(x)=1/x                   g(x)=3x

 

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

 

https://www.khanacademy.org/math/integral-calculus/integration-techniques/integration_by_parts/v/integral-of-ln-x

 

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

Melody  Apr 25, 2015

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