definite integral to evaluation (what am I doing wrong here 3) I was given the below definite integral to evaluate. below is the equation and my answer after I plug in the values but it is wrong. correct answer should be  29/6 what am I doing wrong? thank you
$$\int_1^2 \left(x + \frac 1x\right)^2 \,dx = \int_1^2 x^2 + \left(\frac 1x\right)^2 = \frac {x^3}{3} + \ln |x| = 3.0$$
(Source http://i.stack.imgur.com/V3UDP.jpg)

You expanded incorrectly: Recall
$$(a + b)^2 = a^2 + 2ab + b^2$$
That gives us 
$$\left(x + \frac 1x\right)^2 = x^2 + 2\left(x \cdot \frac 1x\right)  + \frac 1{x^2} =  x^2 + 2 + \frac 1{x^2}$$
Now go ahead and apply the power rule to evaluate the integral.
$$\begin{align} \int_1^2 \left(x + \frac 1x\right)^2 \,dx & = \int_1^2 \left( x^2 + 2 + \frac 1{x^2}\right)\,dx \\ \\ & = \int_1^2 \left( x^2 + 2 + x^{-2}\right)\,dx \\ \\ &= \dfrac {x^3}{3} + 2x - \frac 1x {\Huge|}_1^2\end{align}$$
