Answer
\[\begin{align}
& \text{a}\text{. False}\text{.} \\
& \text{b}\text{. False}\text{.} \\
& \text{c}\text{. False}\text{.} \\
& \text{d}\text{. False}\text{.} \\
\end{align}\]
Work Step by Step
\[\begin{align}
& \text{a}\text{. }\int{\frac{3}{{{x}^{2}}+4}=\int{\frac{3}{{{x}^{2}}}dx}+\int{\frac{3}{4}}dx} \\
& \text{The statement is false, because we cannot add the } \\
& \text{denominators of a rational functions}\text{.} \\
& \\
& \text{b}\text{. }\int{\frac{{{x}^{3}}+2}{3{{x}^{4}}+x}}dx \\
& \text{The statement is false, because this is not an improper rational} \\
& \text{function, the degree of the denominator is greater than the} \\
& \text{numerator}\text{.} \\
& \\
& \text{c}\text{. }\int{\frac{dx}{\sin x+1}=\ln \left| \sin x+1 \right|+C} \\
& \text{The statement is false, because the numerator does not contain} \\
& \text{the derivative the denominator, then the rule does not apply}\text{.} \\
& \\
& \text{d}\text{. }\int{\frac{dx}{{{e}^{x}}}=\ln {{e}^{x}}+C} \\
& \text{The statement is false, }\ln {{e}^{x}}=x\text{ and }\int{\frac{dx}{{{e}^{x}}}\text{ is not }\int{dx}}. \\
\end{align}\]
