If \$f'(x) = 3x^2 sin (1/x) - x cos (1/x)\$, x ≠ 0, f(0) = 0 then the value of \$f(1/x)\$ is?

A) 3

B) 0

C) 1

D) 2

The value of \$\int (log x / (x + 1)^2)\$ dx is.

A) \$ - (log x)/ (x -1) + logx - log(x - 1)\$

B) \$ - (log x)/ (x +1) + logx - log(x +1)\$

C) \$ - (log x)/ (x -1) - logx - log(x +1)\$

D) \$ (log x)/ (x +1) + logx - log(x +1)\$

If \$\int (\sqrt(x))^5 / (\sqrt(x)^7 + x^6)\$ dx = a \$"In" ( x^k / (x^k + 1))\$ + c, then the value of 2k is ?

A) 6

B) 4

C) 3

D) 5

\$\int cos(log_e x)\$ dx is equal to?

A) \$2 (cos(log_e x + sin(log_e x)))\$

B) \$x/2 (cos(log_e x - sin(log_e x)))\$

C) \$2x (cos(log_e x - sin(log_e x)))\$

D) \$x/2 (cos(log_e x + sin(log_e x)))\$

If \$\int (e^x sinx) dx = 1/2 e^x . a + c\$, then a = ?

A) sinx + cosx

B) cosx - sinx

C) sinx - cosx

D) - sinx - cosx

Evaluate \$\int(6x^4 + 3cosx)dx\$.

A) \$(6x^4)/5 + 2sinx + C\$

B) \$(6x^5) + 2sinx + C\$

C) \$(6x^5)/5 + 3sinx + C\$

D) \$(6x^5)/5 - 3sinx + C\$

Evaluate \$\int((x^2 - 1)^2/x^2)dx\$.

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

B) \$1/3 x^3 - 2x - 1/2x + C\$

C) \$1/3 x^3 + x - 1/x + C\$

D) \$1/2 x^2 + 2x - 1/x + C\$

Evaluate \$\int(5/(cos u cot u))"du"\$.

A) 5sec u + C

B) sec u + C

C) 5sin u + C

D) sin u + C

Evaluate the integral \$int (3x^2 + 4x − 5)dx\$.

A) \$x^3 + 2x^2 − 5x\$

B) \$x^3 + 2x^2 − 5x + C\$

C) \$x^3 + 2x^2 − 5x - C\$

D) \$x^3 + 2x^2 − 5x + 7 + C\$

Find the antiderivative of \$6e^2x\$.

A) \$4e^3 x^3/2 + C\$

B) \$3e^2 x^2 + C\$

C) \$3e^2 + x^2 + C\$

D) \$3e^2 - x^2 + C\$