+0  
 
0
606
1
avatar

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

 Apr 24, 2015

Best Answer 

 #1
avatar+95284 
+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 :)

 Apr 25, 2015
 #1
avatar+95284 
+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

13 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.