I=_2^8[3]x+1[3]x+1+[3]11-xdx is equal to : Option 1: 1/2 Option 2: 6 Option 3: 10 Option 4: 3

The answer is '3'. View full solution:

CUET Mathematics - I=_2^8[3]x+1[3]x+1+[3]11-xdx is equal to : | PYQs + Solutions

CUET Mathematics 2026 22nd May Shift 1

Calculus

Medium

applied

$\frac{1}{2}$

✅ Correct Option: 4

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$\int_{\frac{1}{3}}^{1} \frac{(x - x^3)^{\frac{1}{3}}}{x^4} dx =$

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Match List-I with List-II

Where C is arbitrary constant.

List-I	List-II
(A) $\displaystyle\int \dfrac{dx}{x^2 - a^2} =$	(I) $\log\left\vert x + \sqrt{x^2+a^2}\right\vert + C$
(B) $\displaystyle\int \dfrac{dx}{a^2 - x^2} =$	(II) $\log\left\vert x + \sqrt{x^2-a^2}\right\vert + C$
(C) $\displaystyle\int \dfrac{dx}{\sqrt{x^2 - a^2}} =$	(III) $\dfrac{1}{2a}\log\left\vert \dfrac{x-a}{x+a}\right\vert + C$
(D) $\displaystyle\int \dfrac{dx}{\sqrt{x^2 + a^2}} =$	(IV) $\dfrac{1}{2a}\log\left\vert \dfrac{a+x}{a-x}\right\vert + C$

Choose the correct answer from the options given below:

15 June Shift 2

The integral $\int \frac{dx}{x^2(x^4+1)^{\frac{3}{4}}}$ equals __________.