Originally Posted by

**Em Yeu Anh** 1. $\displaystyle \int_1^e\frac{5x^2+x-3}{x}dx $

For this question, I was wondering if dividing the x through all of the terms would be the best way to start solving, which gives:

$\displaystyle = \int_1^e(5x+1-3x^{-1})dx $ and then taking the antiderivative, evaluating from 1 to e etc... Mr F says: Correct.

2. $\displaystyle \int_0^{\frac{\pi}{4}}\frac{d}{dx}(\frac{xtanx}{1+ x})dx $

Also need help starting out this one. For this question does the derivative of $\displaystyle \frac{xtanx}{1+x}$ need to first be taken? I do not know if it would be permissible to pull the d/dx out into the front of the integral, or even if that would help at all.

Additional thanks in advance.