Answer is: option2
\( \frac{7x^2}{2} - 4x - \frac{7}{4} \ln|4x + 7| + C \)Solution:
Using long division method:
We have:
\[ \frac{28x^2 + 33x - 35}{4x + 7} = 7x - 4 + \frac{-7}{4x + 7} \]
Now integrate term by term:
\[ \int \left(7x - 4 + \frac{-7}{4x + 7}\right) dx = \int 7x \, dx - \int 4 \, dx - \int \frac{7}{4x + 7} dx \]
\[ \int \frac{28x^2 + 33x - 35}{4x + 7} dx = \frac{7x^2}{2} - 4x - \frac{7}{4} \ln|4x + 7| + C \]
Hence option B