Question:medium

If $\int \frac{3x+2}{4x^2+4x+5}dx = A\log(4x^2+4x+5)+B\tan^{-1}(\frac{2x+1}{2})+c$, then $A+B=$

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To integrate rational functions of the form $\int \frac{px+q}{ax^2+bx+c}dx$, always start by expressing the numerator as a linear combination of the derivative of the denominator and a constant: $px+q = \lambda(2ax+b) + \mu$. This splits the problem into a logarithm part and an inverse tangent part.

Updated On: Mar 30, 2026

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The Correct Option is A

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