Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

\(\int \frac{3x-2}{\left(x+1\right)^2\left(x+3\right)}dx\) equals 

Options:

\(\frac{4}{11}\log\left|\frac{x+1}{x+3}\right|+\frac{5}{2\left(x+1\right)}+C\)

\(\frac{11}{4}\log\left|\frac{x+1}{x+3}\right|+\frac{5}{2\left(x+1\right)}+C\)

\(\frac{11}{4}\log\left|\frac{x+1}{x+3}\right|-\frac{5}{2\left(x+1\right)}+C\)

\(\frac{11}{4}\log\left|\frac{x+1}{x+3}\right|+\frac{2}{5\left(x+1\right)}+C\)

Correct Answer:

\(\frac{11}{4}\log\left|\frac{x+1}{x+3}\right|+\frac{5}{2\left(x+1\right)}+C\)

Explanation:

USe partial fractions.