JEE Main 2026 · 2 Apr · Shift 2 · Mathematics Q19

← JEE Main 2026 · 2 Apr · Shift 2

MathematicsSingle correct+4 / -1Question 19 of 75

Let $f(x)=\displaystyle\int\left(\frac{16x+24}{x^2+2x-15}\right)dx$ . If $f(4)=14\log_e(3)$ and $f(7)=\log_e\left(2^\alpha\cdot3^\beta\right)$ , $\alpha,\beta\in\mathbb N$ , then $\alpha+\beta$ is equal to :

Answer and worked solution

Official answer: C

Partial fractions. $\dfrac{16x+24}{(x+5)(x-3)}=\dfrac7{x+5}+\dfrac9{x-3}$ , so $f=7\ln|x+5|+9\ln|x-3|+C$ .

Constant. $f(4)=7\ln9+C=14\ln3$ , so $C=0$ .

Value. $f(7)=7\ln12+9\ln4=32\ln2+7\ln3$ , so $\alpha+\beta=39$ .

(C)

Topics:Partial fractions

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JEE Main 2026 · 2 Apr · Shift 2, Mathematics question 19