Why is the Constant 1/2 Used in Evaluating Integrals and Differentials?

[fiziksfun]

Can someone explain to me why \int\frac{x}{x^2+1} = \frac{1}{2}ln(x^2+1) WHERE DOES THE ONE HALF COME FROM ?

 

[Doc Al]

Take the derivative of the right hand side and find out for yourself. (Hint: Chain rule.)

 

[snipez90]

(ln(u))' = \frac{u'}{u}

 

[fiziksfun]

ok none of these responses helped me at all.

 

[Doc Al]

Did you take the derivative of the right hand side?

 

[NoMoreExams]

You can also evaluate the LHS i.e. the integral

Hint #1 - it's a u-subst.

Hint #2 - let u = x^2 + 1

 

[snipez90]

I'm sorry but the OP has no business trying a u-sub if he doesn't follow the first hint. The idea that you can take the derivative to verify the correctness of an integral is fundamental. Remembering to apply the chain rule answers the question. I mean sure, he could apply a technique that really follows from these basic principles but then it would be hard to tell if he actually knew why.