Evaluate the integral: \$ \int (dx/(1+sin(x))) \$.

A) \$ - 3/(tan(x/2) + 1) + C \$

B) \$ - 2/(tan(x/2) + 1) + C \$

C) \$ - 4/(tan(x/2) + 1) + C \$

D) \$ - 6/(tan(x/2) + 1) + C \$

Which of the following is equal to \$ \int (5/(x^2 + 6x + 10)) dx \$?

A) \$ 3tan^(-1)(x^2 + 6x + 10) + C \$

B) \$ 5tan^(-1)(x + 3) + C \$

C) \$ 9tan^(-1)(x + 3) + C \$

D) \$ 5tan^(-1)(x^2 + 6x + 10) + C \$

Evaluate the integral: \$ \int tan^3x sec^5x dx \$.

A)\$ (1/2) sec^7x - (1/5) sec^5x + C \$

B) \$ (1/7) sec^7x - (1/8) sec^5x + C \$

C) \$ (1/7) sec^5x - (1/5) sec^3x + C \$

D) \$ (1/7) sec^7x - (1/5) sec^5x + C \$

\$ \int (x^2 - 2)/(x^3 - 6x + 1) dx \$ =

A) \$ (1/6) ln∣x^3 − 6x + 1∣ + C \$

B) \$ (1/3) ∣x^3 − 4x + 1∣ + C \$

C) \$ (1/2) ln∣x^3 − 6x + 1∣ + C \$

D) \$ (1/3) ln∣x^3 − 6x + 1∣ + C \$

Evaluate the integral: \$ \int (x^2 + 1)/(x^3 + 3x) dx \$.

A) \$ (1/6) ​ln |x(x^2 + 3)| + C \$

B) \$ (1/9) ​ln|x(x^2 + 3)| + C \$

C) \$ (1/3) ​ln|x(x^2 + 3)| + C \$

D) \$ (2/3) ​ln|x(x^3 + 2)| + C \$

Evaluate the integral \$\int (x^2 + 3x + 2)/((x + 1)(x^2 + x + 1)) dx\$

A) \$1/2 ln|4x^2 + 4x + 4| + \sqrt(3) arctan((\sqrt(3)) (2x + 1)) + C\$

B) \$2 ln|4x^2 + 4x + 4| - \sqrt(3) arctan((1/\sqrt(3)) (2x + 1)) + C\$

C) \$1/2 ln|4x^2 + 4x + 4| + \sqrt(3) arctan((1/\sqrt(3)) (2x + 1)) + C\$

D) \$4 ln|4x^2 + 4x + 2| + \sqrt(3) arctan((1/\sqrt(2)) (2x + 1)) + C\$

Find the integral \$\int(ln(x) e^x )dx\$

A) \$ e^x (ln(x) - 1) + C\$

B) \$ e^x ((x) + 1) + C\$

C) \$ e^x ((x) - 1) + C\$

D) \$ e^2x (ln(x) - 1) + C\$

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

A) \$ pi/4 + 1\$

B) \$ pi/2 + 1\$

C) \$ pi \$

D) \$ pi + 1/2\$

Evaluate the definite integral of \$g(x) = 4x^3 - 2x^2 + 3x - 1\$ from x = 1 to x = 3.

A) 64

B) 72.6

C) 86.24

D) 88.34

Determine the integral \$ \int (cos(x)/(1+sin(x))) dx \$.

A) \$ln(2 + sin(x)) + C\$

B) \$ln(1 + sin(x)) + C\$

C) \$ln(2 + sin(2x)) + C\$

D) \$2ln(1 - sin(x)) + C\$