Calculus check - evaluate ∫ dx/2√(x)*(1+x) the 1+x is not under the radical. My sol'n is tan-1√(x) + C

Question

Is this correct or should it be 1/2tan-1√(x) + C

Thanks

Answer 1

You were right the first time: it is simply arctan(√(x)) + C, without the 1/2 coefficient you thought of.

The derivative of arctan(u) is du/(1+u^2). With a u of √(x), our du is equal to 1/(2√(x)), which is present in our integrand, so we want to keep it. If you multiply by 1/2 we'd end up with a 4 in the denominator.

--charlie

Answer 2

Maybe I'm rusty, but I got to 4/15x^(3/2)*(3x+5) + C

Answer 3

yes ur answer is correct
u can check ur answer by differentiating it.
if u can come back to the question then it is definitely correct!