$$\int_{0}^{4} \frac{6x}{\sqrt{2x+1}}\, dx$$
What is the value of the integral?
A) 12
B) 15
C) 18
D) 20
E) 24

The slope of the tangent line to the graph of a function f at $\mathrm { x } = \mathrm { a }$ is $1$, and the slope of the tangent line at $x = b$ is $\sqrt { 3 }$. Given that the second derivative function $\mathbf { f } ^ { \prime \prime } ( \mathbf { x } )$ is continuous on the interval $[ \mathbf { a } , \mathbf { b } ]$, what is the value of
$$\int _ { b } ^ { a } f ^ { \prime } ( x ) \cdot f ^ { \prime \prime } ( x ) d x$$
?
A) - 1
B) 1
C) 2
D) $\frac { 1 } { 3 }$
E) $\frac { 2 } { 3 }$

$$\int _ { 4 } ^ { 9 } \frac { 3 x - 3 } { \sqrt { x } + 1 } d x$$
What is the value of the integral?
A) 13
B) 18
C) 23
D) 28
E) 33

$$\int_{1}^{2} (x+2) \cdot \sqrt[3]{x^{2} + 4x - 4}\, dx$$
What is the value of this integral?
A) $\dfrac{45}{8}$ B) $\dfrac{47}{8}$ C) $\dfrac{49}{8}$ D) $\dfrac{45}{4}$ E) $\dfrac{47}{4}$