Hi

Can someone tell me how would i anti-differentiate the following:

1) $\displaystyle \frac{x}{x+1}$

2) In this question you have to evaluate the following definite integrals:

This is what i done:

$\displaystyle \int_1^5e+\frac{1}{x}dx$

$\displaystyle =e^x+ln(x)$

$\displaystyle =e^5+ln^5-e^1+ln(1)$

$\displaystyle =ln(5)+e^4$

answer was ln(5) +4e but i don't understand how they got it.

P.S