Find the derivative of the function \$f(x) = (2x^2 - 3x + 5)^(3x+2)\$.

A) \$ (3ln(2x^2 + 3x + 5) + ( (4x - 3)(3x + 2))/(2x^2 + 3x + 5) )( (2x^2 + 3x + 5)^(3x+2) )\$

B) \$ (4ln(2x^2 - 3x + 5) + ( (4x - 5)(3x + 2))/(2x^2 - 3x + 5) )( (2x^2 - 3x + 5)^(3x+1) )\$

C) \$ (3ln(2x^2 - 3x + 5) + ( (4x - 3)(3x + 2))/(2x^2 - 3x + 5) )( (2x^2 - 3x + 5)^(3x+2) )\$

D) \$ (3ln(2x^2 - 3x + 5) - ( (4x - 3)(3x + 2))/(2x^2 - 3x + 5) )( (2x^2 - 3x + 5)^(2x+3) )\$

Evaluate the definite integral \$ \int_0^(π/4) tan^2(x) sec^4(x) dx \$.

A) \$ 8/15\$

B) \$ 9/16\$

C) \$ 5/17\$

D) \$ 7/25\$

Consider the following series:
\$\sum_{n=1}^\infty ((n + 1) / (2^n)) \$
Determine whether the series converges or diverges. If it converges, find its sum.

A) Infinity

B) 2

C) 0

D) 4

Perform the division:
\$(-3 + 2i) / (1 - i)\$.

A) \$ (- 5 + i)/2 \$

B) \$ (-5 - i)/2 \$

C) \$ ( 5 - i)/2 \$

D) \$ (5 + 3i)/2 \$

Find the integral of \$ f(x) = (x^2 + 5x + 1)/(x + 2) \$.

A) \$ x + 1/2 (x + 2)^2 - 5ln| x + 2| + 2 \$

B) \$ x + 1/2 (x + 2)^2 + 5ln| x + 2| + 4 \$

C) \$ x - 1/4 (x + 2)^2 - 5ln| x + 2| + 2 \$

D) \$ 2x + 7(x + 2)^2 - 5ln| x + 2| + 7 \$

Find the derivative of the function
\$ m(u) = ( e^4u + (2/u) - u^3 ) \$.

A) \$ 4e^4u - (2/u^3) - 3u^2 \$

B) \$ 4e^4u - (2/u^2) - 3u^2 \$

C) \$ 4e^4u +(2/u^2) - 3u^2 \$

D) \$ 4e^4u + (2/u^2) + 3u^2 \$

Find the derivative of the function
\$ q(w) = ( ln(w^3 + 2w ) - \sqrt(w) + 4w ) \$.

A) \$ ((3w^2 + 2 )/(w^2 + 2w) ) - ( 1/(2\sqrt(w))) + 4 \$

B) \$ ((2w^2 + 2 )/(w^3 + 2w) ) + ( 1/(2\sqrt(w))) - 4 \$

C) \$ ((3w^2 + 2 )/(w^3 + 2w) ) - ( 1/(2\sqrt(w))) + 4 \$

D) \$ ((2w^2 - 2 )/(w^3 + 2w) ) - ( 1/(2\sqrt(w))) + 4 \$

Evaluate the integral \$ \int (3e^x sin (e^x)) dx\$.

A) \$ (3e^x sin (e^x)) - (e^2x cos(e^x) - cos(e^x)) + c\$

B) \$ (3e^2x sin (e^x)) - (e^x cos(e^x) - cos(e^x)) + c\$

C) \$ (3e^x sin (e^2x)) + (e^x cos(e^x) - cos(e^x)) + c\$

D) \$ (3e^x sin (e^x)) - (e^x cos(e^x) - cos(e^x)) + c\$

Evaluate the following infinite series: \$ \sum_{n=1}^\infty ((n^2 + 2) / (n^4 + 4n^2 + 2)) \$.

A) Converges, and its sum is 0.

B) Diverges, and its sum is 1.

C) Converges, and its sum is 1.

D) Diverges, and its sum is 0.

Solve the equation \$ z^2 - 8z + 16 = 0\$ for z.

A) z = 2

B) z = 4

C) z = 3

D) z = 1