antiderivatives

[Marierose]

Find the general antiderivative

___x____
f(x)= x2+1

When i solved this problem i got [(1/2) x^2] *ln(x^2+1) +C but the ans in the back of my book says (1/2) ln(x^2+1) +C What am i doing wrong

 

[stapel]

What am i doing wrong

I have no idea. Please reply showing your steps, so we can try to find the error.

Thank you.

Eliz.

 

[pka]

Often if you cannot see why a function is an antiderivative of another function, it really helps to find the derivative of the proposed answer.

\(\displaystyle \L
f(x) = \left( {1/2} \right)\ln (x^2 + 1)\quad \Rightarrow \quad f'(x) = (1/2)\left( {\frac{{2x}}{{x^2 + 1}}} \right) = \frac{x}{{x^2 + 1}}\)

By studying the above, you should see why the given answer is correct.