I have a set of problems that I don't know how to do. I'm using them to study for my exam, so please show a step-by-step or at least a basic idea how to do it.

1) $\displaystyle \int^5_1 \frac{log_5 x}{x}dx$

2) Evaluate: $\displaystyle lim_{x \to 0} (\frac{1}{ln(x+1)} - \frac{1}{x})$

3) Californium-252 has a half-life of 2.645 years. If the equation describing the decay of the readioactive nuclei is given by $\displaystyle y=y_0e^{kt}$, find:

a) the value of k

b) how long it will take for 95% of the radioactive nuclei to disintegrate.

4) Solve:$\displaystyle \frac{dy}{dx} + y = x$

I don't even know what I'm supposed to do on this one...

5) $\displaystyle \int x^3e^xdx$

6) Use $\displaystyle \frac{dy}{dx} = ky(M-y)$ with k=.001 and M=150 to write y as a function of t. $\displaystyle (y_o = 5)$

Thank you!!!