CUET Mathematics - Value of 2(x-3)sqrt(x+1) dx is: (Here C is an arbitrary constant) | PYQs + Solutions

CUET Mathematics 2025 19 May Shift 1

Calculus

Medium

common

$\log\left|\frac{x-3}{x+1}\right| + C$

$\log\left|\frac{\sqrt{x-1}-2}{\sqrt{x+1}}\right| + C$

$\frac{1}{2}\log\left|\frac{\sqrt{x+1}-1}{\sqrt{x+1}+1}\right| + C$

$\log\left|\frac{\sqrt{x+1}-2}{\sqrt{x+1}+2}\right| + C$

✅ Correct Option: 4

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If $\int e^x\left(\frac{x-1}{(x+1)^3}\right)dx = \frac{Ae^x}{(x+1)^B} + C$ , where C is constant of integration then which of the following are correct?

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(B) $A = 1$

(D) $B = 2$

Choose the correct answer from the options given below:

CUET Mathematics 2025 19 May Shift 1 PYQs

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