Value of dx/(^(3/5)x * ^(7/5)x) is (where c is an arbitrary constant) Option 1: 5/2^(2/5)x + c Option 2: 2/5^(5/2)x + c Option 3: 3/5^(4/5)x + c Option 4: 1/5^(1/5)x + c

Answer: 5/2^(2/5)x + c. Solution: The exponents add to 3/5+7/5=2, so the integrand can be written as (^2 x)/(^(3/5)x). Putting t= x with dt=^2 x dx gives t^(-3/5)dt=5/2t^(2/5)+c=5/2^(2/5)x+c.

Calculus

Integrals

Hard

core

Value of $\displaystyle\int \dfrac{dx}{\sin^{\frac{3}{5}}x \cdot \cos^{\frac{7}{5}}x}$ is (where c is an arbitrary constant)

$\dfrac{5}{2}\tan^{\frac{2}{5}}x + c$

$\dfrac{2}{5}\tan^{\frac{5}{2}}x + c$

$\dfrac{3}{5}\sin^{\frac{4}{5}}x + c$

$\dfrac{1}{5}\cos^{\frac{1}{5}}x + c$

✅ Correct Option: 1

The exponents add to $\frac{3}{5}+\frac{7}{5}=2$ , so the integrand can be written as $\frac{\sec^2 x}{\tan^{3/5}x}$ . Putting $t=\tan x$ with $dt=\sec^2 x\,dx$ gives $\int t^{-3/5}dt=\frac{5}{2}t^{2/5}+c=\frac{5}{2}\tan^{2/5}x+c$ .

2026: 18 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $\displaystyle\int_{\pi/6}^{\pi/3} \cos x \, dx$	(I) $0$
(B) $\displaystyle\int_{-\pi}^{\pi} (\sin^{61}x + x^{123}) \, dx$	(II) $4$
(C) $\displaystyle\int_{0}^{\pi/2} \dfrac{1}{1+\tan^3 x} \, dx$	(III) $\dfrac{\sqrt{3}-1}{2}$
(D) $\displaystyle\int_{-2}^{2} (2 - \left\vert x \right\vert) \, dx$	(IV) $\dfrac{\pi}{4}$

Choose the correct answer from the options given below:

2026: 21 May Shift 1

$\int e^x \left(\frac{x-1}{2x^2}\right) dx$ is equal to ( where $C$ is an arbitrary constant)

2026: 26 May Shift 2

$\displaystyle\int \dfrac{1}{e^x-1}\,dx$ is equal to:

(where C is an arbitrary constant)

2025: 3 June Shift 1

Match List-I with List-II

List-I	List-II
Integral	Value
---	---
(A) $\int_{-1}^{1} (\vert x\vert + 1) dx$	(I) 0
(B) $\int_{-2}^{2} \vert x + 1\vert dx$	(II) 2
(C) $\int_{-1}^{1} 3\vert x^2\vert dx$	(III) 5
(D) $\int_{-1}^{1} x\vert x\vert dx$	(IV) 3

Choose the correct answer from the options given below:

2023: 23 May Shift 3

The integral $\int e^x \left(\frac{x-1}{2x^2}\right) dx$ is equal to:

2025: 27 May Shift 1

$\int \frac{dx}{e^x + e^{-x}}$ is equal to

Value of ∫dxsin⁡35x⋅cos⁡75x\displaystyle\int \dfrac{dx}{\sin^{\frac{3}{5}}x \cdot \cos^{\frac{7}{5}}x}∫sin53​x⋅cos57​xdx​ is (where c is an arbitrary constant)

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Value of $\displaystyle\int \dfrac{dx}{\sin^{\frac{3}{5}}x \cdot \cos^{\frac{7}{5}}x}$ is (where c is an arbitrary constant)