Question

\[\int\frac{x + 7}{3 x^2 + 25x + 28}\text{ dx}\]

Answer 1

\[I = \int\frac{x + 7}{3 x^2 + 25x + 28}dx\]
\[ = \int\frac{x + 7}{3 x^2 + 21x + 4x + 28}dx\]
\[ = \int\frac{x + 7}{3x\left( x + 7 \right) + 4\left( x + 7 \right)}dx\]
\[ = \int\frac{x + 7}{\left( 3x + 4 \right)\left( x + 7 \right)}dx\]

\[= \int\frac{1}{(3x + 4)}dx\]
\[ = \frac{1}{3}\text{ ln }\left| 3x + 4 \right| + c\]