Help Please Integration of Logs (1 Viewer)

[emma011]

Find the integral of:

3x/x^2+7

 

[RealiseNothing]

What's the derivative of the denominator? it's 2x right. So we want the top to be 2x. To do this we times the top by 2/3. We then put 3/2 out the front of the integral to preserve our integral.

 

[abdog]

How about 4/x? How do you integrate that?

 

[RealiseNothing]

How about 4/x? How do you integrate that?

Integrating that is just standard now.

 

[abdog]

But the answer is 4lnx + c. Also, what about 3x/(x^2+7)?

 

[Carrotsticks]

But the answer is 4lnx. Also, what about 3x/(x^2+7)?

 

[abdog]

Can you explain the other one, 4/x?

 

[RealiseNothing]

But the answer is 4lnx + c. Also, what about 3x/(x^2+7)?

 

[abdog]

Ok I finally get it.

 

[Frostbitten]

Can you explain it in more detail please?

Its just a formula to remember, primitive of 1/x = ln(x) and since it's 4 x 1/x it is therefor 4ln(x) and finaly when its an undefined i.e. not between two defined points you have to add the constant C at the end.

 

[emma011]

Thanks everyone for your help

 

[Focus is Key]

I just remember that du/u= ln(u) +C and use Integration by Substitution