What is the Antiderivative of a Complex Square Root Function?

[rwsjyiy]

Homework Statement

Antiderivative of sqrt[e^x+ln(x^2)+1]

Homework Equations

The Attempt at a Solution

(2[(e^x+ln(x^2)+1)^(3/2)]x^2)/[3(e^x+2x)]

 

[HallsofIvy]

No, that is incorrect and I don't think this can by integrated in terms of elementary functions. What you have done, integrating $u^{1/2}$ as $(3/2)u^{3/2}$ and then dividing by the derivative of u, can only be done if u is linear so that u' is a constant. Constants can be "moved" inside and outside of an integral. functions of the variable of integration cannot.