CUET Mathematics - For x > 1, e^7 x - e^5 xe^5 x - e^4 x dx equals. | PYQs + Solutions

CUET Mathematics 2025 15 May Shift 2

Calculus

Medium

core

$\frac{x^3}{3} + \frac{x^2}{2} + C$ ; $C$ is a constant of integration

$\frac{x^3}{3} - \frac{x^2}{2} + C$ ; $C$ is a constant of integration

$\frac{x^3}{6} + \frac{x^2}{4} + C$ ; $C$ is a constant of integration

$\frac{x^3}{6} - \frac{x^2}{4} + C$ ; $C$ is a constant of integration

✅ Correct Option: 1

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$\int_2^5 |x - 3|dx$ equals

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$\int \frac{\log_e x}{(1 + \log_e x)^2} dx$ is equal to

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Match List-I with List-II (Given that $c$ is an arbitrary constant)

List-I	List-II
(A) $\int \frac{dx}{\sqrt{a^2 - x^2}} =$	(I) $\log_e \|x + \sqrt{x^2 - a^2}\| + c$
(B) $\int \sqrt{a^2 - x^2} dx =$	(II) $\sin^{-1} \frac{x}{a} + c$
(C) $\int \sqrt{x^2 - a^2} dx =$	(III) $\frac{x}{2} \sqrt{a^2 - x^2} + \frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(D) $\int \frac{dx}{\sqrt{x^2 - a^2}} =$	(IV) $\frac{x}{2} \sqrt{x^2 - a^2} - \frac{a^2}{2} \log_e \|x + \sqrt{x^2 - a^2}\| + c$

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CUET Mathematics 2025 15 May Shift 2 PYQs