{x+2}{x²-7 x+12} d x is equal to

Correct Answer is : −5log⁡∣x−3∣+6log⁡∣x−4∣+c-5 |x-3|+6 |x-4|+c−5log∣x−3∣+6log∣x−4∣+c

Correct Answer is : −5log⁡∣x−3∣+6log⁡∣x−4∣+c-5 |x-3|+6 |x-4|+c−5log∣x−3∣+6log∣x−4∣+c

Test Index

MHTCET 11 Apr 2026 Shift 1 Paper

Question : 128 of 150

Marks: +1, -0

\int \frac{x+2}{x^{2}-7 x+12} d x

is equal to

Solution:

Concept:

Decompose the given rational function into partial fractions, then integrate each simple term using

\int \frac{1}{x-a} dx = \log |x-a| + c

Explanation:

First factor the denominator:

x^{2}-7x+12=(x-3)(x-4)

Write the integrand in partial fraction form:

\frac{x+2}{(x-3)(x-4)} = \frac{A}{x-3} + \frac{B}{x-4}

Equating numerators gives:

x+2 = A(x-4) + B(x-3)

Put

x=3

5 = A(-1) \Rightarrow A = -5

Put

x=4

6 = B(1) \Rightarrow B = 6

Therefore:

\frac{x+2}{x^{2}-7x+12} = \frac{-5}{x-3} + \frac{6}{x-4}

Now integrate term by term:

\int \frac{x+2}{x^{2}-7x+12} dx = -5\int \frac{dx}{x-3} + 6\int \frac{dx}{x-4}

= -5 \log |x-3| + 6 \log |x-4| + c

Answer:

The integral equals

-5 \log |x-3| + 6 \log |x-4| + c

, which matches Option A.

Go to Question:

Prev Question

Next Question