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1. Find the indefinite integral \(\int \frac{x+1}{x^2 + 2x + 5} dx \)

a.  \(\frac{1}{2} \ln(x^2 + 2x + 5) + c\)

b.  \(\ln(x^2 + 2x + 5) + c\)

c.  \(\frac{\frac{1}{2}x^2 + x}{\frac{1}{3}x^3 + x^2 + 5x} + c\)

d.  \(\frac{1}{2}\frac{\frac{1}{2}x^2 + x}{\frac{1}{3}x^3 + x^2 + 5x} + c\)

e.  \(\frac{1}{2x + 2} + c\)

2. Find the indefinite integral \(\int x\sec^2(x^2) dx \)

a.  \(\tan(x^2) + c\)

b.  \(\frac{1}{2} \tan(x^2) + c\)

c.  \(\frac{1}{3} \sec^3(x^2) + c\)

d.  \(\frac{1}{3} \sec^3(x^3) + c\)

e.  \(\frac{1}{3} \sec^3(\frac{1}{3}x^3) + c\)