Which of the following statements is true?
A. If $f^{\prime}(x)=2$ for all $x$ and if and $f(0)=0$ then $\int f(x) d x=k x+C$ for some constant $C$.
B. $f^{\prime}(x)=2$ for all $x$ and if and $f(0)=0$ then $\int f(x) d x=x^{2}+C$ for some constant $C$.
C. $\int \frac{1}{\ln (x)} d x=\ln |\ln (x)|+C$ for some constant $C$.
D. If $\int f(x) d x=C$ then $f(x)=C+x$ for some constant $C$.

Step 1 ：Analyze each option:

Step 2 ：A. If $f^{\prime}(x)=2$ for all $x$ and if and $f(0)=0$ then $\int f(x) d x=k x+C$ for some constant $C$. This statement is saying that the integral of a function whose derivative is always 2 and passes through the origin is a linear function. This is not necessarily true. The integral of a function whose derivative is always 2 is a function of the form $2x + C$, not $kx + C$.

Step 3 ：B. $f^{\prime}(x)=2$ for all $x$ and if and $f(0)=0$ then $\int f(x) d x=x^{2}+C$ for some constant $C$. This statement is saying that the integral of a function whose derivative is always 2 and passes through the origin is a quadratic function. This is true. The integral of a function whose derivative is always 2 is a function of the form $2x + C$, and if $f(0) = 0$, then $C = 0$, so the integral is indeed $2x$, which is a special case of $x^2 + C$.

Step 4 ：C. $\int \frac{1}{\ln (x)} d x=\ln |\ln (x)|+C$ for some constant $C$. This statement is saying that the integral of $1/\ln(x)$ is $\ln|\ln(x)| + C$. This is not true. The integral of $1/\ln(x)$ is a special function called the logarithmic integral, denoted as $\text{li}(x)$, not $\ln|\ln(x)| + C$.

Step 5 ：D. If $\int f(x) d x=C$ then $f(x)=C+x$ for some constant $C$. This statement is saying that if the integral of a function is a constant, then the function is a linear function. This is not true. If the integral of a function is a constant, then the function is a constant function, not a linear function.

Step 6 ：So, the only true statement is B.

Step 7 ：Final Answer: \(\boxed{B}\)